quoracle/quorums/expr.py

275 lines
8.1 KiB
Python
Raw Normal View History

2021-01-22 22:47:07 +00:00
from typing import Dict, Iterator, Generic, List, Optional, Set, TypeVar
2021-01-30 01:46:00 +00:00
import datetime
2021-01-22 22:47:07 +00:00
import itertools
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]':
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])
return _or(self, rhs)
def __mul__(self, rhs: 'Expr[T]') -> 'Expr[T]':
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])
return _and(self, rhs)
def quorums(self) -> Iterator[Set[T]]:
raise NotImplementedError
# TODO(mwhittaker): Add a function to return minimal quorums.
# TODO(mwhittaker): Add a function to check whether two expressions are
# equal. One simple way to do this is compare the set of minimal quorums.
# There might be more efficient ways to check if two expressions are equal.
2021-01-22 22:47:07 +00:00
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,
2021-01-30 01:46:00 +00:00
write_capacity: Optional[float] = None,
latency: datetime.timedelta = None) -> None:
2021-01-22 22:47:07 +00:00
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)')
2021-01-30 01:46:00 +00:00
if latency is None:
self.latency = datetime.timedelta(seconds=1)
else:
self.latency = latency
2021-01-22 22:47:07 +00:00
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:
subfailures = [e._dup_free_min_failures() for e in self.es]
return sum(sorted(subfailures)[:len(subfailures) - self.k + 1])
2021-01-22 22:47:07 +00:00
def choose(k: int, es: List[Expr[T]]) -> Expr[T]:
2021-01-31 20:31:22 +00:00
if len(es) == 0:
raise ValueError('no expressions provided')
if not (1 <= k <= len(es)):
raise ValueError('k must be in the range [1, len(es)]')
2021-01-22 22:47:07 +00:00
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]:
2021-01-31 20:31:22 +00:00
if len(es) == 0:
raise ValueError('no expressions provided')
2021-01-22 22:47:07 +00:00
return choose(len(es) // 2 + 1, es)