183 lines
7 KiB
Python
183 lines
7 KiB
Python
# TODO(mwhittaker): We can define a set of read quorums that are not minimal.
|
|
# Does this mess things up?
|
|
|
|
from . import distribution
|
|
from .distribution import Distribution
|
|
from .expr import Expr, Node
|
|
from .strategy import ExplicitStrategy, Strategy
|
|
from typing import Dict, Iterator, Generic, List, Optional, Set, TypeVar
|
|
import collections
|
|
import itertools
|
|
import pulp
|
|
|
|
|
|
T = TypeVar('T')
|
|
|
|
|
|
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:
|
|
optimal_writes = reads.dual()
|
|
if not all(optimal_writes.is_quorum(write_quorum)
|
|
for write_quorum in writes.quorums()):
|
|
raise ValueError(
|
|
'Not all read quorums intersect all write 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 = distribution.canonicalize_rw(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 capacity(self,
|
|
read_fraction: Optional[Distribution] = None,
|
|
write_fraction: Optional[Distribution] = None,
|
|
f: int = 0) \
|
|
-> float:
|
|
return 1 / self.load(read_fraction, write_fraction, f)
|
|
|
|
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])
|