Added optimal load strategy with LP.

quorums/quorums.py

@@ -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.
+        # TODO(mwhittaker): Allow read_fraction or write_fraction.
-        reads = list(self.read_quorums())
+        # TODO(mwhittaker): Implement independent strategy.
-        writes = list(self.write_quorums())
+        return self._load_optimal_strategy(
-        return ExplicitStrategy(reads, [1 / len(reads)] * len(reads),
+                    _canonicalize_distribution(read_fraction))
-                                writes, [1 / len(writes)] * len(writes))
 
     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:
+    def load(self, read_fraction: Distribution) -> float:
-        raise NotImplementedError
+        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)
+# grid = QuorumSystem(reads=a*b*c + d*e*f + g*h*i)
-sigma = grid.strategy(0.1)
+# sigma = grid.strategy(0.1)
-for _ in range(10):
+# print(grid)
-    print(sigma.get_write_quorum())
+# 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?