 
Summary: THE PROBABILISTIC ANALYSIS OF A HEURISTIC FOR THE
ASSIGNMENT PROBLEM
David Avis
C. W. Lai*
School of Computer Science
McGill University
805 Sherbrooke St. W.
Montreal, Canada, H3A 2K6
ABSTRACT
We present a heuristic to solve the m by m assignment problem in O(m 2 ) time.
The assignment problem is formulated as a weighted complete bipartite graph
G = (S, T , E) , S = T  = m. For convenience we assume that m is even. The main pro
cedure in the heuristic is to construct a graph G d = (S, T , E d ) which is a subgraph of
G , E d  = 4dn , n = m
2 , such that we can find a perfect matching in G d with probabil
ity at least 1  1
3
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č
d
