ON THE FLUCTUATION IN THE RANDOM ASSIGNMENT PROBLEM Lee, Sung-Chul; Su, Zhong-Gen;
Consider the random assignment (or bipartite matching) problem with iid uniform edge costs t(i, j). Let be the optimal assignment cost. Just recently does Aldous  give a rigorous proof that E longrightarrowζ(2). In this paper we establish the upper and lower bounds for Var , i.e., there exist two strictly positive but finite constants and such athat 2)/ (log n)2)/ Var (log n).EX>.
assignment problem;bipartite matching matching;conditional variance;probabilistic analysis of algorithms;