Split up code into separate modules.
This commit is contained in:
Michael Whittaker
parent
630effa405
commit
7f1a1a3934
7 changed files with 577 additions and 562 deletions
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@ -1,4 +1,4 @@
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from quorums.quorums import *
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from quorums import *
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a = Node('a')
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b = Node('b')
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@ -0,0 +1,2 @@
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from .expr import Node, choose, majority
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from .quorum_system import QuorumSystem
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57
quorums/distribution.py
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57
quorums/distribution.py
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@ -0,0 +1,57 @@
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from typing import Dict, Optional, Union
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Fraction = float
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Weight = float
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Probability = float
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Distribution = Union[
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# For example, 1 means 100% reads.
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int,
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# For example, 0.25 means 25% reads.
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float,
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# For example, {0.25: 1, 0.8: 2} means 25% reads one third of the time and
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# 80% reads two thirds of the time.
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Dict[Fraction, Weight],
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]
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def canonicalize(d: Distribution) -> Dict[Fraction, Probability]:
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if isinstance(d, int):
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if d < 0 or d > 1:
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raise ValueError('distribution must be in the range [0, 1]')
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return {float(d): 1.}
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elif isinstance(d, float):
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if d < 0 or d > 1:
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raise ValueError('distribution must be in the range [0, 1]')
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return {d: 1.}
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elif isinstance(d, dict):
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if len(d) == 0:
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raise ValueError('distribution cannot empty')
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if any(weight < 0 for weight in d.values()):
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raise ValueError('distribution cannot have negative weights')
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total_weight = sum(d.values())
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if total_weight == 0:
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raise ValueError('distribution cannot have zero weight')
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return {float(f): weight / total_weight
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for (f, weight) in d.items()
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if weight > 0}
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else:
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raise ValueError('distribution must be an int, a float, a Dict[float, '
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'float] or a List[Tuple[float, float]]')
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def canonicalize_rw(read_fraction: Optional[Distribution],
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write_fraction: Optional[Distribution]) \
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-> Dict[Fraction, Probability]:
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if read_fraction is None and write_fraction is None:
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raise ValueError('Either read_fraction or write_fraction must be given')
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elif read_fraction is not None and write_fraction is not None:
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raise ValueError('Only one of read_fraction or write_fraction can be '
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'given')
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elif read_fraction is not None:
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return canonicalize(read_fraction)
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else:
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assert write_fraction is not None
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return {1 - f: weight
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for (f, weight) in canonicalize(write_fraction).items()}
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250
quorums/expr.py
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250
quorums/expr.py
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@ -0,0 +1,250 @@
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from typing import Dict, Iterator, Generic, List, Optional, Set, TypeVar
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import itertools
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import pulp
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T = TypeVar('T')
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def _min_hitting_set(sets: Iterator[Set[T]]) -> int:
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x_vars: Dict[T, pulp.LpVariable] = dict()
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next_id = itertools.count()
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problem = pulp.LpProblem("min_hitting_set", pulp.LpMinimize)
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for (i, xs) in enumerate(sets):
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for x in xs:
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if x not in x_vars:
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id = next(next_id)
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x_vars[x] = pulp.LpVariable(f'x{id}', cat=pulp.LpBinary)
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problem += sum(x_vars[x] for x in xs) >= 1
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problem += sum(x_vars.values())
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problem.solve(pulp.apis.PULP_CBC_CMD(msg=False))
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return int(sum(v.varValue for v in x_vars.values()))
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class Expr(Generic[T]):
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def __add__(self, rhs: 'Expr[T]') -> 'Expr[T]':
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def _or(lhs: Expr[T], rhs: Expr[T]) -> 'Or[T]':
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if isinstance(lhs, Or) and isinstance(rhs, Or):
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return Or(lhs.es + rhs.es)
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elif isinstance(lhs, Or):
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return Or(lhs.es + [rhs])
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elif isinstance(rhs, Or):
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return Or([lhs] + rhs.es)
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else:
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return Or([lhs, rhs])
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return _or(self, rhs)
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def __mul__(self, rhs: 'Expr[T]') -> 'Expr[T]':
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def _and(lhs: Expr[T], rhs: Expr[T]) -> 'And[T]':
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if isinstance(lhs, And) and isinstance(rhs, And):
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return And(lhs.es + rhs.es)
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elif isinstance(lhs, And):
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return And(lhs.es + [rhs])
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elif isinstance(rhs, And):
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return And([lhs] + rhs.es)
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else:
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return And([lhs, rhs])
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return _and(self, rhs)
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def quorums(self) -> Iterator[Set[T]]:
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raise NotImplementedError
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def is_quorum(self, xs: Set[T]) -> bool:
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raise NotImplementedError
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def elements(self) -> Set[T]:
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return {node.x for node in self.nodes()}
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def nodes(self) -> Set['Node[T]']:
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raise NotImplementedError
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def resilience(self) -> int:
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if self.dup_free():
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return self._dup_free_min_failures() - 1
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else:
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return _min_hitting_set(self.quorums()) - 1
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def dual(self) -> 'Expr[T]':
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raise NotImplementedError
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def dup_free(self) -> bool:
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return len(self.nodes()) == self._num_leaves()
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def _num_leaves(self) -> int:
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raise NotImplementedError
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def _dup_free_min_failures(self) -> int:
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raise NotImplementedError
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class Node(Expr[T]):
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def __init__(self,
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x: T,
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capacity: Optional[float] = None,
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read_capacity: Optional[float] = None,
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write_capacity: Optional[float] = None) -> None:
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self.x = x
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# A user either specifies capacity or (read_capacity and
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# write_capacity), but not both.
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if (capacity is None and
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read_capacity is None and
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write_capacity is None):
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self.read_capacity = 1.0
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self.write_capacity = 1.0
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elif (capacity is not None and
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read_capacity is None and
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write_capacity is None):
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self.read_capacity = capacity
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self.write_capacity = capacity
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elif (capacity is None and
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read_capacity is not None and
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write_capacity is not None):
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self.read_capacity = read_capacity
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self.write_capacity = write_capacity
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else:
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raise ValueError('You must specify capacity or (read_capacity '
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'and write_capacity)')
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def __str__(self) -> str:
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return str(self.x)
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def __repr__(self) -> str:
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return f'Node({self.x})'
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def quorums(self) -> Iterator[Set[T]]:
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yield {self.x}
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def is_quorum(self, xs: Set[T]) -> bool:
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return self.x in xs
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def nodes(self) -> Set['Node[T]']:
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return {self}
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def dual(self) -> Expr:
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return self
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def _num_leaves(self) -> int:
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return 1
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def _dup_free_min_failures(self) -> int:
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return 1
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class Or(Expr[T]):
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def __init__(self, es: List[Expr[T]]) -> None:
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if len(es) == 0:
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raise ValueError(f'Or cannot be constructed with an empty list')
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self.es = es
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def __str__(self) -> str:
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return '(' + ' + '.join(str(e) for e in self.es) + ')'
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def __repr__(self) -> str:
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return f'Or({self.es})'
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def quorums(self) -> Iterator[Set[T]]:
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for e in self.es:
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yield from e.quorums()
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def is_quorum(self, xs: Set[T]) -> bool:
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return any(e.is_quorum(xs) for e in self.es)
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def nodes(self) -> Set[Node[T]]:
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return set.union(*[e.nodes() for e in self.es])
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def dual(self) -> Expr:
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return And([e.dual() for e in self.es])
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def _num_leaves(self) -> int:
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return sum(e._num_leaves() for e in self.es)
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def _dup_free_min_failures(self) -> int:
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return sum(e._dup_free_min_failures() for e in self.es)
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class And(Expr[T]):
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def __init__(self, es: List[Expr[T]]) -> None:
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if len(es) == 0:
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raise ValueError(f'And cannot be constructed with an empty list')
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self.es = es
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def __str__(self) -> str:
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return '(' + ' * '.join(str(e) for e in self.es) + ')'
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def __repr__(self) -> str:
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return f'And({self.es})'
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def quorums(self) -> Iterator[Set[T]]:
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for subquorums in itertools.product(*[e.quorums() for e in self.es]):
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yield set.union(*subquorums)
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def is_quorum(self, xs: Set[T]) -> bool:
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return all(e.is_quorum(xs) for e in self.es)
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def nodes(self) -> Set[Node[T]]:
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return set.union(*[e.nodes() for e in self.es])
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def dual(self) -> Expr:
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return Or([e.dual() for e in self.es])
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def _num_leaves(self) -> int:
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return sum(e._num_leaves() for e in self.es)
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def _dup_free_min_failures(self) -> int:
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return min(e._dup_free_min_failures() for e in self.es)
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class Choose(Expr[T]):
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def __init__(self, k: int, es: List[Expr[T]]) -> None:
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if k <= 0 or k > len(es):
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raise ValueError(f'k must be in the range [1, {len(es)}]')
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self.k = k
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self.es = es
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def __str__(self) -> str:
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return f'choose{self.k}(' + ', '.join(str(e) for e in self.es) + ')'
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def __repr__(self) -> str:
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return f'Chose({self.k}, {self.es})'
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def quorums(self) -> Iterator[Set[T]]:
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for combo in itertools.combinations(self.es, self.k):
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for subquorums in itertools.product(*[e.quorums() for e in combo]):
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yield set.union(*subquorums)
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def is_quorum(self, xs: Set[T]) -> bool:
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return sum(1 if e.is_quorum(xs) else 0 for e in self.es) >= self.k
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def nodes(self) -> Set[Node[T]]:
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return set.union(*[e.nodes() for e in self.es])
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def dual(self) -> Expr:
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# TODO(mwhittaker): Prove that this is in fact the dual.
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return Choose(len(self.es) - self.k + 1, [e.dual() for e in self.es])
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def _num_leaves(self) -> int:
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return sum(e._num_leaves() for e in self.es)
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def _dup_free_min_failures(self) -> int:
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return sum(sorted(e._dup_free_min_failures() for e in self.es)[:self.k])
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def choose(k: int, es: List[Expr[T]]) -> Expr[T]:
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if k == 1:
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return Or(es)
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elif k == len(es):
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return And(es)
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else:
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return Choose(k, es)
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def majority(es: List[Expr[T]]) -> Expr[T]:
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return choose(len(es) // 2 + 1, es)
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174
quorums/quorum_system.py
Normal file
174
quorums/quorum_system.py
Normal file
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@ -0,0 +1,174 @@
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# TODO(mwhittaker): We can define a set of read quorums that are not minimal.
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# Does this mess things up?
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from . import distribution
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from .distribution import Distribution
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from .expr import Expr, Node
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from .strategy import ExplicitStrategy, Strategy
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from typing import Dict, Iterator, Generic, List, Optional, Set, TypeVar
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import collections
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import itertools
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import pulp
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T = TypeVar('T')
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class QuorumSystem(Generic[T]):
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def __init__(self, reads: Optional[Expr[T]] = None,
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writes: Optional[Expr[T]] = None) -> None:
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if reads is not None and writes is not None:
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# TODO(mwhittaker): Think of ways to make this more efficient.
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assert all(len(r & w) > 0
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for (r, w) in itertools.product(reads.quorums(),
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writes.quorums()))
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self.reads = reads
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self.writes = writes
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elif reads is not None and writes is None:
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self.reads = reads
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self.writes = reads.dual()
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elif reads is None and writes is not None:
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self.reads = writes.dual()
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self.writes = writes
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else:
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raise ValueError('A QuorumSystem must be instantiated with a set '
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'of read quorums or a set of write quorums')
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def __repr__(self) -> str:
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return f'QuorumSystem(reads={self.reads}, writes={self.writes})'
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def read_quorums(self) -> Iterator[Set[T]]:
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return self.reads.quorums()
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def write_quorums(self) -> Iterator[Set[T]]:
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return self.writes.quorums()
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def is_read_quorum(self, xs: Set[T]) -> bool:
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return self.reads.is_quorum(xs)
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def is_write_quorum(self, xs: Set[T]) -> bool:
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return self.writes.is_quorum(xs)
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def nodes(self) -> Set[Node[T]]:
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return self.reads.nodes() | self.writes.nodes()
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def resilience(self) -> int:
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return min(self.read_resilience(), self.write_resilience())
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def read_resilience(self) -> int:
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return self.reads.resilience()
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def write_resilience(self) -> int:
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return self.writes.resilience()
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def strategy(self,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) \
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-> 'Strategy[T]':
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if f < 0:
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raise ValueError('f must be >= 0')
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d = distribution.canonicalize_rw(read_fraction, write_fraction)
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if f == 0:
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return self._load_optimal_strategy(
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list(self.read_quorums()),
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list(self.write_quorums()),
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d)
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else:
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xs = [node.x for node in self.nodes()]
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read_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
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write_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
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if len(read_quorums) == 0:
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raise ValueError(f'There are no {f}-resilient read quorums')
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if len(write_quorums) == 0:
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raise ValueError(f'There are no {f}-resilient write quorums')
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return self._load_optimal_strategy(read_quorums, write_quorums, d)
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def dup_free(self) -> bool:
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return self.reads.dup_free() and self.writes.dup_free()
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def _f_resilient_quorums(self,
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f: int,
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xs: List[T],
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e: Expr) -> Iterator[Set[T]]:
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assert f >= 1
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def helper(s: Set[T], i: int) -> Iterator[Set[T]]:
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if all(e.is_quorum(s - set(failure))
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for failure in itertools.combinations(s, min(f, len(s)))):
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yield set(s)
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return
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for j in range(i, len(xs)):
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s.add(xs[j])
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yield from helper(s, j + 1)
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s.remove(xs[j])
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return helper(set(), 0)
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def load(self,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) \
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-> float:
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sigma = self.strategy(read_fraction, write_fraction, f)
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return sigma.load(read_fraction, write_fraction)
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def _load_optimal_strategy(self,
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read_quorums: List[Set[T]],
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write_quorums: List[Set[T]],
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read_fraction: Dict[float, float]) \
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-> 'Strategy[T]':
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# TODO(mwhittaker): Explain f_r calculation.
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fr = sum(f * weight for (f, weight) in read_fraction.items())
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nodes = self.reads.nodes() | self.writes.nodes()
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read_capacity = {node.x: node.read_capacity for node in nodes}
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write_capacity = {node.x: node.write_capacity for node in nodes}
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read_quorum_vars: List[pulp.LpVariable] = []
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x_to_read_quorum_vars: Dict[T, List[pulp.LpVariable]] = \
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collections.defaultdict(list)
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for (i, read_quorum) in enumerate(read_quorums):
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v = pulp.LpVariable(f'r{i}', 0, 1)
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read_quorum_vars.append(v)
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for x in read_quorum:
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x_to_read_quorum_vars[x].append(v)
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||||
write_quorum_vars: List[pulp.LpVariable] = []
|
||||
x_to_write_quorum_vars: Dict[T, List[pulp.LpVariable]] = \
|
||||
collections.defaultdict(list)
|
||||
for (i, write_quorum) in enumerate(write_quorums):
|
||||
v = pulp.LpVariable(f'w{i}', 0, 1)
|
||||
write_quorum_vars.append(v)
|
||||
for x in write_quorum:
|
||||
x_to_write_quorum_vars[x].append(v)
|
||||
|
||||
# Form the linear program to find the load.
|
||||
problem = pulp.LpProblem("load", pulp.LpMinimize)
|
||||
|
||||
# If we're trying to balance the strategy, then we want to minimize the
|
||||
# pairwise absolute differences between the read probabilities and the
|
||||
# write probabilities.
|
||||
l = pulp.LpVariable('l', 0, 1)
|
||||
problem += l
|
||||
problem += (sum(read_quorum_vars) == 1, 'valid read strategy')
|
||||
problem += (sum(write_quorum_vars) == 1, 'valid write strategy')
|
||||
for node in nodes:
|
||||
x = node.x
|
||||
x_load: pulp.LpAffineExpression = 0
|
||||
if x in x_to_read_quorum_vars:
|
||||
x_load += fr * sum(x_to_read_quorum_vars[x]) / read_capacity[x]
|
||||
if x in x_to_write_quorum_vars:
|
||||
x_load += ((1 - fr) * sum(x_to_write_quorum_vars[x]) /
|
||||
write_capacity[x])
|
||||
problem += (x_load <= l, x)
|
||||
|
||||
problem.solve(pulp.apis.PULP_CBC_CMD(msg=False))
|
||||
return ExplicitStrategy(nodes,
|
||||
read_quorums,
|
||||
[v.varValue for v in read_quorum_vars],
|
||||
write_quorums,
|
||||
[v.varValue for v in write_quorum_vars])
|
||||
|
|
@ -1,567 +1,6 @@
|
|||
# TODO(mwhittaker): We can define a set of read quorums that are not minimal.
|
||||
# Does this mess things up?
|
||||
|
||||
from typing import (Dict, Iterator, Generic, List, Optional, Set, Tuple,
|
||||
TypeVar, Union)
|
||||
import collections
|
||||
import itertools
|
||||
import numpy as np
|
||||
import pulp
|
||||
|
||||
|
||||
T = TypeVar('T')
|
||||
|
||||
|
||||
def _min_hitting_set(sets: Iterator[Set[T]]) -> int:
|
||||
x_vars: Dict[T, pulp.LpVariable] = dict()
|
||||
next_id = itertools.count()
|
||||
|
||||
problem = pulp.LpProblem("min_hitting_set", pulp.LpMinimize)
|
||||
for (i, xs) in enumerate(sets):
|
||||
for x in xs:
|
||||
if x not in x_vars:
|
||||
id = next(next_id)
|
||||
x_vars[x] = pulp.LpVariable(f'x{id}', cat=pulp.LpBinary)
|
||||
problem += sum(x_vars[x] for x in xs) >= 1
|
||||
|
||||
problem += sum(x_vars.values())
|
||||
problem.solve(pulp.apis.PULP_CBC_CMD(msg=False))
|
||||
return int(sum(v.varValue for v in x_vars.values()))
|
||||
|
||||
|
||||
class Expr(Generic[T]):
|
||||
def __add__(self, rhs: 'Expr[T]') -> 'Expr[T]':
|
||||
return _or(self, rhs)
|
||||
|
||||
def __mul__(self, rhs: 'Expr[T]') -> 'Expr[T]':
|
||||
return _and(self, rhs)
|
||||
|
||||
def quorums(self) -> Iterator[Set[T]]:
|
||||
raise NotImplementedError
|
||||
|
||||
def is_quorum(self, xs: Set[T]) -> bool:
|
||||
raise NotImplementedError
|
||||
|
||||
def elements(self) -> Set[T]:
|
||||
return {node.x for node in self.nodes()}
|
||||
|
||||
def nodes(self) -> Set['Node[T]']:
|
||||
raise NotImplementedError
|
||||
|
||||
def resilience(self) -> int:
|
||||
if self.dup_free():
|
||||
return self._dup_free_min_failures() - 1
|
||||
else:
|
||||
return _min_hitting_set(self.quorums()) - 1
|
||||
|
||||
def dual(self) -> 'Expr[T]':
|
||||
raise NotImplementedError
|
||||
|
||||
def dup_free(self) -> bool:
|
||||
return len(self.nodes()) == self._num_leaves()
|
||||
|
||||
def _num_leaves(self) -> int:
|
||||
raise NotImplementedError
|
||||
|
||||
def _dup_free_min_failures(self) -> int:
|
||||
raise NotImplementedError
|
||||
|
||||
|
||||
class Node(Expr[T]):
|
||||
def __init__(self,
|
||||
x: T,
|
||||
capacity: Optional[float] = None,
|
||||
read_capacity: Optional[float] = None,
|
||||
write_capacity: Optional[float] = None) -> None:
|
||||
self.x = x
|
||||
|
||||
# A user either specifies capacity or (read_capacity and
|
||||
# write_capacity), but not both.
|
||||
if (capacity is None and
|
||||
read_capacity is None and
|
||||
write_capacity is None):
|
||||
self.read_capacity = 1.0
|
||||
self.write_capacity = 1.0
|
||||
elif (capacity is not None and
|
||||
read_capacity is None and
|
||||
write_capacity is None):
|
||||
self.read_capacity = capacity
|
||||
self.write_capacity = capacity
|
||||
elif (capacity is None and
|
||||
read_capacity is not None and
|
||||
write_capacity is not None):
|
||||
self.read_capacity = read_capacity
|
||||
self.write_capacity = write_capacity
|
||||
else:
|
||||
raise ValueError('You must specify capacity or (read_capacity '
|
||||
'and write_capacity)')
|
||||
|
||||
def __str__(self) -> str:
|
||||
return str(self.x)
|
||||
|
||||
def __repr__(self) -> str:
|
||||
return f'Node({self.x})'
|
||||
|
||||
def quorums(self) -> Iterator[Set[T]]:
|
||||
yield {self.x}
|
||||
|
||||
def is_quorum(self, xs: Set[T]) -> bool:
|
||||
return self.x in xs
|
||||
|
||||
def nodes(self) -> Set['Node[T]']:
|
||||
return {self}
|
||||
|
||||
def dual(self) -> Expr:
|
||||
return self
|
||||
|
||||
def _num_leaves(self) -> int:
|
||||
return 1
|
||||
|
||||
def _dup_free_min_failures(self) -> int:
|
||||
return 1
|
||||
|
||||
|
||||
class Or(Expr[T]):
|
||||
def __init__(self, es: List[Expr[T]]) -> None:
|
||||
if len(es) == 0:
|
||||
raise ValueError(f'Or cannot be constructed with an empty list')
|
||||
|
||||
self.es = es
|
||||
|
||||
def __str__(self) -> str:
|
||||
return '(' + ' + '.join(str(e) for e in self.es) + ')'
|
||||
|
||||
def __repr__(self) -> str:
|
||||
return f'Or({self.es})'
|
||||
|
||||
def quorums(self) -> Iterator[Set[T]]:
|
||||
for e in self.es:
|
||||
yield from e.quorums()
|
||||
|
||||
def is_quorum(self, xs: Set[T]) -> bool:
|
||||
return any(e.is_quorum(xs) for e in self.es)
|
||||
|
||||
def nodes(self) -> Set[Node[T]]:
|
||||
return set.union(*[e.nodes() for e in self.es])
|
||||
|
||||
def dual(self) -> Expr:
|
||||
return And([e.dual() for e in self.es])
|
||||
|
||||
def _num_leaves(self) -> int:
|
||||
return sum(e._num_leaves() for e in self.es)
|
||||
|
||||
def _dup_free_min_failures(self) -> int:
|
||||
return sum(e._dup_free_min_failures() for e in self.es)
|
||||
|
||||
|
||||
class And(Expr[T]):
|
||||
def __init__(self, es: List[Expr[T]]) -> None:
|
||||
if len(es) == 0:
|
||||
raise ValueError(f'And cannot be constructed with an empty list')
|
||||
|
||||
self.es = es
|
||||
|
||||
def __str__(self) -> str:
|
||||
return '(' + ' * '.join(str(e) for e in self.es) + ')'
|
||||
|
||||
def __repr__(self) -> str:
|
||||
return f'And({self.es})'
|
||||
|
||||
def quorums(self) -> Iterator[Set[T]]:
|
||||
for subquorums in itertools.product(*[e.quorums() for e in self.es]):
|
||||
yield set.union(*subquorums)
|
||||
|
||||
def is_quorum(self, xs: Set[T]) -> bool:
|
||||
return all(e.is_quorum(xs) for e in self.es)
|
||||
|
||||
def nodes(self) -> Set[Node[T]]:
|
||||
return set.union(*[e.nodes() for e in self.es])
|
||||
|
||||
def dual(self) -> Expr:
|
||||
return Or([e.dual() for e in self.es])
|
||||
|
||||
def _num_leaves(self) -> int:
|
||||
return sum(e._num_leaves() for e in self.es)
|
||||
|
||||
def _dup_free_min_failures(self) -> int:
|
||||
return min(e._dup_free_min_failures() for e in self.es)
|
||||
|
||||
class Choose(Expr[T]):
|
||||
def __init__(self, k: int, es: List[Expr[T]]) -> None:
|
||||
if k <= 0 or k > len(es):
|
||||
raise ValueError(f'k must be in the range [1, {len(es)}]')
|
||||
|
||||
self.k = k
|
||||
self.es = es
|
||||
|
||||
def __str__(self) -> str:
|
||||
return f'choose{self.k}(' + ', '.join(str(e) for e in self.es) + ')'
|
||||
|
||||
def __repr__(self) -> str:
|
||||
return f'Chose({self.k}, {self.es})'
|
||||
|
||||
def quorums(self) -> Iterator[Set[T]]:
|
||||
for combo in itertools.combinations(self.es, self.k):
|
||||
for subquorums in itertools.product(*[e.quorums() for e in combo]):
|
||||
yield set.union(*subquorums)
|
||||
|
||||
def is_quorum(self, xs: Set[T]) -> bool:
|
||||
return sum(1 if e.is_quorum(xs) else 0 for e in self.es) >= self.k
|
||||
|
||||
def nodes(self) -> Set[Node[T]]:
|
||||
return set.union(*[e.nodes() for e in self.es])
|
||||
|
||||
def dual(self) -> Expr:
|
||||
# TODO(mwhittaker): Prove that this is in fact the dual.
|
||||
return Choose(len(self.es) - self.k + 1, [e.dual() for e in self.es])
|
||||
|
||||
def _num_leaves(self) -> int:
|
||||
return sum(e._num_leaves() for e in self.es)
|
||||
|
||||
def _dup_free_min_failures(self) -> int:
|
||||
return sum(sorted(e._dup_free_min_failures() for e in self.es)[:self.k])
|
||||
|
||||
|
||||
def _and(lhs: Expr[T], rhs: Expr[T]) -> 'And[T]':
|
||||
if isinstance(lhs, And) and isinstance(rhs, And):
|
||||
return And(lhs.es + rhs.es)
|
||||
elif isinstance(lhs, And):
|
||||
return And(lhs.es + [rhs])
|
||||
elif isinstance(rhs, And):
|
||||
return And([lhs] + rhs.es)
|
||||
else:
|
||||
return And([lhs, rhs])
|
||||
|
||||
|
||||
def _or(lhs: Expr[T], rhs: Expr[T]) -> 'Or[T]':
|
||||
if isinstance(lhs, Or) and isinstance(rhs, Or):
|
||||
return Or(lhs.es + rhs.es)
|
||||
elif isinstance(lhs, Or):
|
||||
return Or(lhs.es + [rhs])
|
||||
elif isinstance(rhs, Or):
|
||||
return Or([lhs] + rhs.es)
|
||||
else:
|
||||
return Or([lhs, rhs])
|
||||
|
||||
|
||||
def choose(k: int, es: List[Expr[T]]) -> Expr[T]:
|
||||
if k == 1:
|
||||
return Or(es)
|
||||
elif k == len(es):
|
||||
return And(es)
|
||||
else:
|
||||
return Choose(k, es)
|
||||
|
||||
|
||||
def majority(es: List[Expr[T]]) -> Expr[T]:
|
||||
return choose(len(es) // 2 + 1, es)
|
||||
|
||||
|
||||
ReadFraction = float
|
||||
ReadWriteFraction = float
|
||||
Weight = float
|
||||
Probability = float
|
||||
Distribution = Union[
|
||||
# For example, 1 means 100% reads.
|
||||
int,
|
||||
# For example, 0.25 means 25% reads.
|
||||
float,
|
||||
# For example, {0.25: 1, 0.8: 2} means 25% reads one third of the time and
|
||||
# 80% reads two thirds of the time.
|
||||
Dict[ReadWriteFraction, Weight],
|
||||
]
|
||||
|
||||
|
||||
def _canonicalize_distribution(d: Distribution) \
|
||||
-> Dict[ReadWriteFraction, Probability]:
|
||||
if isinstance(d, int):
|
||||
if d < 0 or d > 1:
|
||||
raise ValueError('distribution must be in the range [0, 1]')
|
||||
return {float(d): 1.}
|
||||
elif isinstance(d, float):
|
||||
if d < 0 or d > 1:
|
||||
raise ValueError('distribution must be in the range [0, 1]')
|
||||
return {d: 1.}
|
||||
elif isinstance(d, dict):
|
||||
if len(d) == 0:
|
||||
raise ValueError('distribution cannot empty')
|
||||
|
||||
if any(weight < 0 for weight in d.values()):
|
||||
raise ValueError('distribution cannot have negative weights')
|
||||
|
||||
total_weight = sum(d.values())
|
||||
if total_weight == 0:
|
||||
raise ValueError('distribution cannot have zero weight')
|
||||
|
||||
return {float(f): weight / total_weight
|
||||
for (f, weight) in d.items()
|
||||
if weight > 0}
|
||||
else:
|
||||
raise ValueError('distribution must be an int, a float, a Dict[float, '
|
||||
'float] or a List[Tuple[float, float]]')
|
||||
|
||||
|
||||
def _canonicalize_rw_distribution(read_fraction: Optional[Distribution],
|
||||
write_fraction: Optional[Distribution]) \
|
||||
-> Dict[ReadFraction, Probability]:
|
||||
if read_fraction is None and write_fraction is None:
|
||||
raise ValueError('Either read_fraction or write_fraction must be given')
|
||||
elif read_fraction is not None and write_fraction is not None:
|
||||
raise ValueError('Only one of read_fraction or write_fraction can be '
|
||||
'given')
|
||||
elif read_fraction is not None:
|
||||
return _canonicalize_distribution(read_fraction)
|
||||
else:
|
||||
assert write_fraction is not None
|
||||
return {1 - f: weight
|
||||
for (f, weight) in
|
||||
_canonicalize_distribution(write_fraction).items()}
|
||||
|
||||
|
||||
class QuorumSystem(Generic[T]):
|
||||
def __init__(self, reads: Optional[Expr[T]] = None,
|
||||
writes: Optional[Expr[T]] = None) -> None:
|
||||
if reads is not None and writes is not None:
|
||||
# TODO(mwhittaker): Think of ways to make this more efficient.
|
||||
assert all(len(r & w) > 0
|
||||
for (r, w) in itertools.product(reads.quorums(),
|
||||
writes.quorums()))
|
||||
self.reads = reads
|
||||
self.writes = writes
|
||||
elif reads is not None and writes is None:
|
||||
self.reads = reads
|
||||
self.writes = reads.dual()
|
||||
elif reads is None and writes is not None:
|
||||
self.reads = writes.dual()
|
||||
self.writes = writes
|
||||
else:
|
||||
raise ValueError('A QuorumSystem must be instantiated with a set '
|
||||
'of read quorums or a set of write quorums')
|
||||
|
||||
def __repr__(self) -> str:
|
||||
return f'QuorumSystem(reads={self.reads}, writes={self.writes})'
|
||||
|
||||
def read_quorums(self) -> Iterator[Set[T]]:
|
||||
return self.reads.quorums()
|
||||
|
||||
def write_quorums(self) -> Iterator[Set[T]]:
|
||||
return self.writes.quorums()
|
||||
|
||||
def is_read_quorum(self, xs: Set[T]) -> bool:
|
||||
return self.reads.is_quorum(xs)
|
||||
|
||||
def is_write_quorum(self, xs: Set[T]) -> bool:
|
||||
return self.writes.is_quorum(xs)
|
||||
|
||||
def nodes(self) -> Set[Node[T]]:
|
||||
return self.reads.nodes() | self.writes.nodes()
|
||||
|
||||
def resilience(self) -> int:
|
||||
return min(self.read_resilience(), self.write_resilience())
|
||||
|
||||
def read_resilience(self) -> int:
|
||||
return self.reads.resilience()
|
||||
|
||||
def write_resilience(self) -> int:
|
||||
return self.writes.resilience()
|
||||
|
||||
def strategy(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None,
|
||||
f: int = 0) \
|
||||
-> 'Strategy[T]':
|
||||
if f < 0:
|
||||
raise ValueError('f must be >= 0')
|
||||
|
||||
d = _canonicalize_rw_distribution(read_fraction, write_fraction)
|
||||
if f == 0:
|
||||
return self._load_optimal_strategy(
|
||||
list(self.read_quorums()),
|
||||
list(self.write_quorums()),
|
||||
d)
|
||||
else:
|
||||
xs = [node.x for node in self.nodes()]
|
||||
read_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
|
||||
write_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
|
||||
if len(read_quorums) == 0:
|
||||
raise ValueError(f'There are no {f}-resilient read quorums')
|
||||
if len(write_quorums) == 0:
|
||||
raise ValueError(f'There are no {f}-resilient write quorums')
|
||||
return self._load_optimal_strategy(read_quorums, write_quorums, d)
|
||||
|
||||
def dup_free(self) -> bool:
|
||||
return self.reads.dup_free() and self.writes.dup_free()
|
||||
|
||||
def _f_resilient_quorums(self,
|
||||
f: int,
|
||||
xs: List[T],
|
||||
e: Expr) -> Iterator[Set[T]]:
|
||||
assert f >= 1
|
||||
|
||||
def helper(s: Set[T], i: int) -> Iterator[Set[T]]:
|
||||
if all(e.is_quorum(s - set(failure))
|
||||
for failure in itertools.combinations(s, min(f, len(s)))):
|
||||
yield set(s)
|
||||
return
|
||||
|
||||
for j in range(i, len(xs)):
|
||||
s.add(xs[j])
|
||||
yield from helper(s, j + 1)
|
||||
s.remove(xs[j])
|
||||
|
||||
return helper(set(), 0)
|
||||
|
||||
def load(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None,
|
||||
f: int = 0) \
|
||||
-> float:
|
||||
sigma = self.strategy(read_fraction, write_fraction, f)
|
||||
return sigma.load(read_fraction, write_fraction)
|
||||
|
||||
def _load_optimal_strategy(self,
|
||||
read_quorums: List[Set[T]],
|
||||
write_quorums: List[Set[T]],
|
||||
read_fraction: Dict[float, float]) \
|
||||
-> 'Strategy[T]':
|
||||
# TODO(mwhittaker): Explain f_r calculation.
|
||||
fr = sum(f * weight for (f, weight) in read_fraction.items())
|
||||
|
||||
nodes = self.reads.nodes() | self.writes.nodes()
|
||||
read_capacity = {node.x: node.read_capacity for node in nodes}
|
||||
write_capacity = {node.x: node.write_capacity for node in nodes}
|
||||
|
||||
read_quorum_vars: List[pulp.LpVariable] = []
|
||||
x_to_read_quorum_vars: Dict[T, List[pulp.LpVariable]] = \
|
||||
collections.defaultdict(list)
|
||||
|
||||
for (i, read_quorum) in enumerate(read_quorums):
|
||||
v = pulp.LpVariable(f'r{i}', 0, 1)
|
||||
read_quorum_vars.append(v)
|
||||
for x in read_quorum:
|
||||
x_to_read_quorum_vars[x].append(v)
|
||||
|
||||
write_quorum_vars: List[pulp.LpVariable] = []
|
||||
x_to_write_quorum_vars: Dict[T, List[pulp.LpVariable]] = \
|
||||
collections.defaultdict(list)
|
||||
for (i, write_quorum) in enumerate(write_quorums):
|
||||
v = pulp.LpVariable(f'w{i}', 0, 1)
|
||||
write_quorum_vars.append(v)
|
||||
for x in write_quorum:
|
||||
x_to_write_quorum_vars[x].append(v)
|
||||
|
||||
# Form the linear program to find the load.
|
||||
problem = pulp.LpProblem("load", pulp.LpMinimize)
|
||||
|
||||
# If we're trying to balance the strategy, then we want to minimize the
|
||||
# pairwise absolute differences between the read probabilities and the
|
||||
# write probabilities.
|
||||
l = pulp.LpVariable('l', 0, 1)
|
||||
problem += l
|
||||
problem += (sum(read_quorum_vars) == 1, 'valid read strategy')
|
||||
problem += (sum(write_quorum_vars) == 1, 'valid write strategy')
|
||||
for node in nodes:
|
||||
x = node.x
|
||||
x_load: pulp.LpAffineExpression = 0
|
||||
if x in x_to_read_quorum_vars:
|
||||
x_load += fr * sum(x_to_read_quorum_vars[x]) / read_capacity[x]
|
||||
if x in x_to_write_quorum_vars:
|
||||
x_load += ((1 - fr) * sum(x_to_write_quorum_vars[x]) /
|
||||
write_capacity[x])
|
||||
problem += (x_load <= l, x)
|
||||
|
||||
problem.solve(pulp.apis.PULP_CBC_CMD(msg=False))
|
||||
return ExplicitStrategy(nodes,
|
||||
read_quorums,
|
||||
[v.varValue for v in read_quorum_vars],
|
||||
write_quorums,
|
||||
[v.varValue for v in write_quorum_vars])
|
||||
|
||||
|
||||
class Strategy(Generic[T]):
|
||||
def load(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) \
|
||||
-> float:
|
||||
raise NotImplementedError
|
||||
|
||||
def get_read_quorum(self) -> Set[T]:
|
||||
raise NotImplementedError
|
||||
|
||||
def get_write_quorum(self) -> Set[T]:
|
||||
raise NotImplementedError
|
||||
|
||||
|
||||
class ExplicitStrategy(Strategy[T]):
|
||||
def __init__(self,
|
||||
nodes: Set[Node[T]],
|
||||
reads: List[Set[T]],
|
||||
read_weights: List[float],
|
||||
writes: List[Set[T]],
|
||||
write_weights: List[float]) -> None:
|
||||
self.nodes = nodes
|
||||
self.read_capacity = {node.x: node.read_capacity for node in nodes}
|
||||
self.write_capacity = {node.x: node.write_capacity for node in nodes}
|
||||
self.reads = reads
|
||||
self.read_weights = read_weights
|
||||
self.writes = writes
|
||||
self.write_weights = write_weights
|
||||
|
||||
def __str__(self) -> str:
|
||||
non_zero_reads = {tuple(r): p
|
||||
for (r, p) in zip(self.reads, self.read_weights)
|
||||
if p > 0}
|
||||
non_zero_writes = {tuple(w): p
|
||||
for (w, p) in zip(self.writes, self.write_weights)
|
||||
if p > 0}
|
||||
return (f'ExplicitStrategy(reads={non_zero_reads}, ' +
|
||||
f'writes={non_zero_writes})')
|
||||
|
||||
def __repr__(self) -> str:
|
||||
return (f'ExplicitStrategy(nodes={self.nodes}, '+
|
||||
f'reads={self.reads}, ' +
|
||||
f'read_weights={self.read_weights},' +
|
||||
f'writes={self.writes}, ' +
|
||||
f'write_weights={self.write_weights})')
|
||||
|
||||
def load(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) \
|
||||
-> float:
|
||||
d = _canonicalize_rw_distribution(read_fraction, write_fraction)
|
||||
fr = sum(f * weight for (f, weight) in d.items())
|
||||
|
||||
read_load: Dict[T, float] = collections.defaultdict(float)
|
||||
for (read_quorum, weight) in zip(self.reads, self.read_weights):
|
||||
for x in read_quorum:
|
||||
read_load[x] += weight
|
||||
|
||||
write_load: Dict[T, float] = collections.defaultdict(float)
|
||||
for (write_quorum, weight) in zip(self.writes, self.write_weights):
|
||||
for x in write_quorum:
|
||||
write_load[x] += weight
|
||||
|
||||
loads: List[float] = []
|
||||
for node in self.nodes:
|
||||
x = node.x
|
||||
load = 0.0
|
||||
if x in read_load:
|
||||
load += fr * read_load[x] / self.read_capacity[x]
|
||||
if x in write_load:
|
||||
load += (1 - fr) * write_load[x] / self.write_capacity[x]
|
||||
loads.append(load)
|
||||
|
||||
return max(loads)
|
||||
|
||||
# TODO(mwhittaker): Add read/write load and capacity and read/write cap.
|
||||
|
||||
def get_read_quorum(self) -> Set[T]:
|
||||
return np.random.choice(self.reads, p=self.read_weights)
|
||||
|
||||
def get_write_quorum(self) -> Set[T]:
|
||||
return np.random.choice(self.writes, p=self.write_weights)
|
||||
|
||||
|
||||
|
||||
|
||||
# a = Node('a')
|
||||
|
|
|
|||
93
quorums/strategy.py
Normal file
93
quorums/strategy.py
Normal file
|
|
@ -0,0 +1,93 @@
|
|||
from . import distribution
|
||||
from .distribution import Distribution
|
||||
from .expr import Node
|
||||
from typing import Dict, Generic, List, Optional, Set, TypeVar
|
||||
import collections
|
||||
import numpy as np
|
||||
|
||||
|
||||
T = TypeVar('T')
|
||||
|
||||
|
||||
class Strategy(Generic[T]):
|
||||
def load(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) \
|
||||
-> float:
|
||||
raise NotImplementedError
|
||||
|
||||
def get_read_quorum(self) -> Set[T]:
|
||||
raise NotImplementedError
|
||||
|
||||
def get_write_quorum(self) -> Set[T]:
|
||||
raise NotImplementedError
|
||||
|
||||
|
||||
class ExplicitStrategy(Strategy[T]):
|
||||
def __init__(self,
|
||||
nodes: Set[Node[T]],
|
||||
reads: List[Set[T]],
|
||||
read_weights: List[float],
|
||||
writes: List[Set[T]],
|
||||
write_weights: List[float]) -> None:
|
||||
self.nodes = nodes
|
||||
self.read_capacity = {node.x: node.read_capacity for node in nodes}
|
||||
self.write_capacity = {node.x: node.write_capacity for node in nodes}
|
||||
self.reads = reads
|
||||
self.read_weights = read_weights
|
||||
self.writes = writes
|
||||
self.write_weights = write_weights
|
||||
|
||||
def __str__(self) -> str:
|
||||
non_zero_reads = {tuple(r): p
|
||||
for (r, p) in zip(self.reads, self.read_weights)
|
||||
if p > 0}
|
||||
non_zero_writes = {tuple(w): p
|
||||
for (w, p) in zip(self.writes, self.write_weights)
|
||||
if p > 0}
|
||||
return (f'ExplicitStrategy(reads={non_zero_reads}, ' +
|
||||
f'writes={non_zero_writes})')
|
||||
|
||||
def __repr__(self) -> str:
|
||||
return (f'ExplicitStrategy(nodes={self.nodes}, '+
|
||||
f'reads={self.reads}, ' +
|
||||
f'read_weights={self.read_weights},' +
|
||||
f'writes={self.writes}, ' +
|
||||
f'write_weights={self.write_weights})')
|
||||
|
||||
def load(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) \
|
||||
-> float:
|
||||
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
||||
fr = sum(f * weight for (f, weight) in d.items())
|
||||
|
||||
read_load: Dict[T, float] = collections.defaultdict(float)
|
||||
for (read_quorum, weight) in zip(self.reads, self.read_weights):
|
||||
for x in read_quorum:
|
||||
read_load[x] += weight
|
||||
|
||||
write_load: Dict[T, float] = collections.defaultdict(float)
|
||||
for (write_quorum, weight) in zip(self.writes, self.write_weights):
|
||||
for x in write_quorum:
|
||||
write_load[x] += weight
|
||||
|
||||
loads: List[float] = []
|
||||
for node in self.nodes:
|
||||
x = node.x
|
||||
load = 0.0
|
||||
if x in read_load:
|
||||
load += fr * read_load[x] / self.read_capacity[x]
|
||||
if x in write_load:
|
||||
load += (1 - fr) * write_load[x] / self.write_capacity[x]
|
||||
loads.append(load)
|
||||
|
||||
return max(loads)
|
||||
|
||||
# TODO(mwhittaker): Add read/write load and capacity and read/write cap.
|
||||
|
||||
def get_read_quorum(self) -> Set[T]:
|
||||
return np.random.choice(self.reads, p=self.read_weights)
|
||||
|
||||
def get_write_quorum(self) -> Set[T]:
|
||||
return np.random.choice(self.writes, p=self.write_weights)
|
||||
Loading…
Reference in a new issue