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graph_manager.py
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graph_manager.py
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import collections
import networkx as nx
import random
import numpy as np
import types
import cvxpy as cp
from mpi4py import MPI
"""
GraphProcessor
:description: GraphProcessor is designed to preprocess the communication graph,
It specifies the activated neighbors of each node at each iteration
"""
class GraphProcessor(object):
def __init__(self, base_graph, commBudget, rank, size, iterations, issubgraph):
self.rank = rank # index of worker
self.size = size # totoal number of workers
self.comm = MPI.COMM_WORLD
self.commBudget = commBudget # user defined budget
if issubgraph:
# if the base graph is already decomposed
self.base_graph = self.getGraphFromSub(base_graph)
self.subGraphs = base_graph
else:
# else: decompose the base graph
self.base_graph = base_graph
self.subGraphs = self.getSubGraphs()
# get Laplacian matrices for subgraphs
self.L_matrices = self.graphToLaplacian()
# get neighbors' index
self.neighbors_info = self.drawer()
def getProbability(self):
""" compute activation probabilities for subgraphs """
raise NotImplemented
def getAlpha(self):
""" compute mixing weights """
raise NotImplemented
def set_flags(self, iterations):
""" generate activation flags for each iteration """
raise NotImplemented
def getGraphFromSub(self, subGraphs):
G = nx.Graph()
for edge in subGraphs:
G.add_edges_from(edge)
return G
def getSubGraphs(self):
""" Decompose the base graph into matchings """
G = self.base_graph
subgraphs = list()
# first try to get as many maximal matchings as possible
for i in range(self.size-1):
M1 = nx.max_weight_matching(G)
if nx.is_perfect_matching(G, M1):
G.remove_edges_from(list(M1))
subgraphs.append(list(M1))
else:
edge_list = list(G.edges)
random.shuffle(edge_list)
G.remove_edges_from(edge_list)
G.add_edges_from(edge_list)
# use greedy algorithm to decompose the remaining part
rpart = self.decomposition(list(G.edges))
for sgraph in rpart:
subgraphs.append(sgraph)
return subgraphs
def graphToLaplacian(self):
L_matrices = list()
for i, subgraph in enumerate(self.subGraphs):
tmp_G = nx.Graph()
tmp_G.add_edges_from(subgraph)
L_matrices.append(nx.laplacian_matrix(tmp_G, list(range(self.size))).todense())
return L_matrices
def decomposition(self, graph):
size = self.size
node_degree = [[i, 0] for i in range(size)]
node_to_node = [[] for i in range(size)]
node_degree_dict = collections.defaultdict(int)
node_set = set()
for edge in graph:
node1, node2 = edge[0], edge[1]
node_degree[node1][1] += 1
node_degree[node2][1] += 1
if node1 in node_to_node[node2] or node2 in node_to_node[node1]:
print("Invalid input graph! Double edge! ("+str(node1) +", "+ str(node2)+")")
exit()
if node1 == node2:
print("Invalid input graph! Circle! ("+str(node1) +", "+ str(node2)+")")
exit()
node_to_node[node1].append(node2)
node_to_node[node2].append(node1)
node_degree_dict[node1] += 1
node_degree_dict[node2] += 1
node_set.add(node1)
node_set.add(node2)
node_degree = sorted(node_degree, key = lambda x: x[1])
node_degree[:] = node_degree[::-1]
subgraphs = []
min_num = node_degree[0][1]
while node_set:
subgraph = []
for i in range(size):
node1, node1_degree = node_degree[i]
if node1 not in node_set:
continue
for j in range(i+1, size):
node2, node2_degree = node_degree[j]
if node2 in node_set and node2 in node_to_node[node1]:
subgraph.append((node1, node2))
node_degree[j][1] -= 1
node_degree[i][1] -= 1
node_degree_dict[node1] -= 1
node_degree_dict[node2] -= 1
node_to_node[node1].remove(node2)
node_to_node[node2].remove(node1)
node_set.remove(node1)
node_set.remove(node2)
break
subgraphs.append(subgraph)
for node in node_degree_dict:
if node_degree_dict[node] > 0:
node_set.add(node)
node_degree = sorted(node_degree, key = lambda x: x[1])
node_degree[:] = node_degree[::-1]
return subgraphs
def drawer(self):
"""
input graph: list[list[tuples]]
[graph1, graph2,...]
graph: [edge1, edge2, ...]
edge: (node1, node2)
output connect: matrix: [[]]
"""
connect = []
cnt = 1
for graph in self.subGraphs:
new_connect = [-1 for i in range(self.size)]
for edge in graph:
node1, node2 = edge[0], edge[1]
if new_connect[node1] != -1 or new_connect[node2] != -1:
print("invalide graph! graph: "+str(cnt))
exit()
new_connect[node1] = node2
new_connect[node2] = node1
# print(new_connect)
connect.append(new_connect)
cnt += 1
return connect
class FixedProcessor(GraphProcessor):
""" wrapper for fixed communication graph """
def __init__(self, base_graph, commBudget, rank, size, iterations, issubgraph):
super(FixedProcessor, self).__init__(base_graph, commBudget, rank, size, iterations, issubgraph)
self.probabilities = self.getProbability()
self.neighbor_weight = self.getAlpha()
self.active_flags = self.set_flags(iterations + 1)
def getProbability(self):
""" activation probabilities are same for subgraphs """
return self.commBudget
def getAlpha(self):
""" there is an analytical expression of alpha in this case """
L_base = np.zeros((self.size, self.size))
for subLMatrix in self.L_matrices:
L_base += subLMatrix
w_b, _ = np.linalg.eig(L_base)
lambdaList = list(sorted(w_b))
if len(w_b) > 1:
alpha = 2 / (lambdaList[1] + lambdaList[-1])
return alpha
def set_flags(self, iterations):
""" warning: np.random.seed should be same across workers
so that the activation flags are same
"""
iterProb = np.random.binomial(1, self.probabilities, iterations)
flags = list()
idx = 0
for prob in iterProb:
if idx % 2 == 0:
flags.append([0,1])
else:
flags.append([1,0])
idx += 1
# flags.append([prob for i in range(len(self.L_matrices))])
return flags
class MatchaProcessor(GraphProcessor):
""" Wrapper for MATCHA
At each iteration, only a random subset of subgraphs are activated
"""
def __init__(self, base_graph, commBudget, rank, size, iterations, issubgraph):
super(MatchaProcessor, self).__init__(base_graph, commBudget, rank, size, iterations, issubgraph)
self.probabilities = self.getProbability()
self.neighbor_weight = self.getAlpha()
self.active_flags = self.set_flags(iterations + 1)
def getProbability(self):
num_subgraphs = len(self.L_matrices)
p = cp.Variable(num_subgraphs)
L = p[0]*self.L_matrices[0]
for i in range(num_subgraphs-1):
L += p[i+1]*self.L_matrices[i+1]
eig = cp.lambda_sum_smallest(L, 2)
sum_p = p[0]
for i in range(num_subgraphs-1):
sum_p += p[i+1]
# cvx optimization for activation probabilities
obj_fn = eig
constraint = [sum_p <= num_subgraphs*self.commBudget, p>=0, p<=1]
problem = cp.Problem(cp.Maximize(obj_fn), constraint)
problem.solve(solver='CVXOPT', kktsolver=cp.ROBUST_KKTSOLVER)
# get solution
tmp_p = p.value
originActivationRatio = np.zeros((num_subgraphs))
for i, pval in enumerate(tmp_p):
originActivationRatio[i] = np.real(float(pval))
return np.minimum(originActivationRatio, 1)
def getAlpha(self):
num_subgraphs = len(self.L_matrices)
num_nodes = self.size
# prepare matrices
I = np.eye(num_nodes)
J = np.ones((num_nodes, num_nodes))/num_nodes
mean_L = np.zeros((num_nodes,num_nodes))
var_L = np.zeros((num_nodes,num_nodes))
for i in range(num_subgraphs):
val = self.probabilities[i]
mean_L += self.L_matrices[i]*val
var_L += self.L_matrices[i]*(1-val)*val
# SDP for mixing weight
a = cp.Variable()
b = cp.Variable()
s = cp.Variable()
obj_fn = s
constraint = [(1-s)*I - 2*a*mean_L-J + b*(np.dot(mean_L,mean_L)+2*var_L) << 0, a>=0, s>=0, b>=0, cp.square(a) <= b]
problem = cp.Problem(cp.Minimize(obj_fn), constraint)
problem.solve(solver='CVXOPT', kktsolver=cp.ROBUST_KKTSOLVER)
return float(a.value)
def set_flags(self, iterations):
""" warning: np.random.seed should be same across workers
so that the activation flags are same
"""
flags = list()
for i in range(len(self.L_matrices)):
flags.append(np.random.binomial(1, self.probabilities[i], iterations))
return [list(x) for x in zip(*flags)]