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Added optimal load strategy with LP.

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Michael Whittaker 2021-01-20 17:59:46 -08:00
parent efbeb8dc44
commit 11fe478c2b
1 changed files with 110 additions and 12 deletions
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122
quorums/quorums.py
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@ -1,5 +1,6 @@
from typing import (Dict, Iterator, Generic, List, Optional, Set, Tuple,
TypeVar, Union)
import collections
import itertools
import numpy as np
import pulp
@ -212,11 +213,10 @@ class QuorumSystem(Generic[T]):
return f'QuorumSystem(reads={self.reads}, writes={self.writes})'
def strategy(self, read_fraction: Distribution) -> 'Strategy[T]':
# TODO(mwhittaker): Implement.
reads = list(self.read_quorums())
writes = list(self.write_quorums())
return ExplicitStrategy(reads, [1 / len(reads)] * len(reads),
writes, [1 / len(writes)] * len(writes))
# TODO(mwhittaker): Allow read_fraction or write_fraction.
# TODO(mwhittaker): Implement independent strategy.
return self._load_optimal_strategy(
_canonicalize_distribution(read_fraction))
def is_read_quorum(self, xs: Set[T]) -> bool:
return self.reads.is_quorum(xs)
@ -227,9 +227,58 @@ class QuorumSystem(Generic[T]):
def write_quorums(self) -> Iterator[Set[T]]:
return self.writes.quorums()
def _load_optimal_strategy(self,
read_fraction: Dict[float, float]) -> \
'Strategy[T]':
fr = sum(f * weight for (f, weight) in read_fraction.items())
reads = list(self.read_quorums())
writes = list(self.write_quorums())
read_load: Dict[T, List[pulp.LpVariable]] = collections.defaultdict(list)
read_weights: List[pulp.LpVariable] = []
for (i, r) in enumerate(reads):
v = pulp.LpVariable(f'r{i}', 0, 1)
read_weights.append(v)
for node in r:
read_load[node].append(v)
write_load: Dict[T, List[pulp.LpVariable]] = collections.defaultdict(list)
write_weights: List[pulp.LpVariable] = []
for (i, r) in enumerate(writes):
v = pulp.LpVariable(f'w{i}', 0, 1)
write_weights.append(v)
for node in r:
write_load[node].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_weights) == 1, 'valid read strategy')
problem += (sum(write_weights) == 1, 'valid write strategy')
for node in read_load.keys() | write_load.keys():
node_load: pulp.LpAffineExpression = 0
if node in read_load:
node_load += fr * sum(read_load[node])
if node in write_load:
node_load += (1 - fr) * sum(write_load[node])
problem += (node_load <= l, node)
# print(problem)
problem.solve(pulp.apis.PULP_CBC_CMD(msg=False))
return ExplicitStrategy(reads, [v.varValue for v in read_weights],
writes, [v.varValue for v in write_weights])
# for v in read_weights + write_weights:
# print(f'{v.name} = {v.varValue}')
# return l.varValue
class Strategy(Generic[T]):
def load(self, read_fraction: Distribution) -> int:
def load(self, read_fraction: Distribution) -> float:
raise NotImplementedError
def get_read_quorum(self) -> Set[T]:
@ -250,10 +299,48 @@ class ExplicitStrategy(Strategy[T]):
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(reads={self.reads}, ' +
f'read_weights={self.read_weights},' +
f'writes={self.writes}, ' +
f'write_weights={self.write_weights})')
# TODO(mwhittaker): Implement __str__ and __repr__.
def load(self, read_fraction: Distribution) -> int:
raise NotImplementedError
def load(self, read_fraction: Distribution) -> float:
d = _canonicalize_distribution(read_fraction)
fr = sum(f * weight for (f, weight) in d.items())
read_load: Dict[T, float] = collections.defaultdict(float)
for (r, p) in zip(self.reads, self.read_weights):
for node in r:
read_load[node] += p
write_load: Dict[T, float] = collections.defaultdict(float)
for (w, p) in zip(self.writes, self.write_weights):
for node in w:
write_load[node] += p
node_loads: List[float] = []
for node in read_load.keys() | write_load.keys():
node_load = 0.0
if node in read_load:
node_load += fr * read_load[node]
if node in write_load:
node_load += (1 - fr) * write_load[node]
node_loads.append(node_load)
return max(node_loads)
def get_read_quorum(self) -> Set[T]:
return np.random.choice(self.reads, p=self.read_weights)
@ -271,10 +358,21 @@ f = Node('f')
g = Node('g')
h = Node('h')
i = Node('i')
grid = QuorumSystem(reads=a*b*c + d*e*f + g*h*i)
sigma = grid.strategy(0.1)
for _ in range(10):
print(sigma.get_write_quorum())
# grid = QuorumSystem(reads=a*b*c + d*e*f + g*h*i)
# sigma = grid.strategy(0.1)
# print(grid)
# print(sigma)
wpaxos = QuorumSystem(reads=majority([majority([a, b, c]),
majority([d, e, f]),
majority([g, h, i])]))
sigma_1 = wpaxos.strategy(read_fraction=0.1)
sigma_5 = wpaxos.strategy(read_fraction=0.5)
sigma_9 = wpaxos.strategy(read_fraction=0.9)
sigma_even = wpaxos.strategy(read_fraction={0.1: 2, 0.5: 2, 0.9: 1})
for sigma in [sigma_1, sigma_5, sigma_9, sigma_even]:
frs = [0.1, 0.5, 0.9, {0.1: 2, 0.5: 2, 0.9: 1}]
print([sigma.load(fr) for fr in frs])
# - num_quorums
# - has dups?