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http://dx.doi.org/10.4134/CKMS.2002.17.2.321

ON THE FLUCTUATION IN THE RANDOM ASSIGNMENT PROBLEM  

Lee, Sung-Chul (Department of Mathematics Yonsei University)
Su, Zhong-Gen (Department of Mathematics Zhejiang University, Department of Mathematics Yonsei University)
Publication Information
Communications of the Korean Mathematical Society / v.17, no.2, 2002 , pp. 321-330 More about this Journal
Abstract
Consider the random assignment (or bipartite matching) problem with iid uniform edge costs t(i, j). Let $A_{n}$ be the optimal assignment cost. Just recently does Aldous [2] give a rigorous proof that E $A_{n}$ longrightarrowζ(2). In this paper we establish the upper and lower bounds for Var $A_{n}$ , i.e., there exist two strictly positive but finite constants $C_1$ and $C_2$ such athat $C_1$ $n^{(-5}$2)/ (log n)$^{(-3}$2)/ $\leq$ Var $A_{n}$ $\leq$ $C_2$ $n^{-1}$ (log n)$^2$.EX>.
Keywords
assignment problem; bipartite matching matching; conditional variance; probabilistic analysis of algorithms;
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  • Reference
1 On the expected value of a random assignment problem /
[ D.W.Walkup ] / SIAM J.Comput.   DOI
2 Probabilistic analysis of heuristics /
[ R.M.Karp;J.M.Steele ] / The Traveling Salesman Problem
3 The ?(2) limit in the random assignment problem /
[] / Random Struct.Alg.
4 Constructive bounds and exact expectations for the random assignment problem /
[ D.Coppersmith;G.B.Sorkin ] / Random Struct.Alg.   DOI   ScienceOn
5 Asymptotic properties of random assignment problems /
[ B.Olin ] / Ph.D.thesis, Kungl Tekniska Hogskolan
6 A Lower bound on the expected cost of an optimal assignemnt /
[ M.X.Goemans;M.S.Kodiallam ] / Math.Oper.Res.   DOI   ScienceOn
7 The assignment problem with uniform (0, 1) cost matrix /
[ A.J.Lazarus ] / B.A.thesis, Department of Mathematics, Princeton University
8 /
[ J.M.Steele ] / Probability Theory and Combinatorial Optimization
9 Asymptotics in the random assignment problem /
[ D.J.Aldous ] / Probab.Theory Relat.Fields   DOI
10 The probabilistic relationship between the assignment and asymmetric traveling salesman problems /
[ A.M.Frieze;G.B.Sorkin ] / Proceedings of SODA
11 Concentration of measure and isoperimetric inequalities in product spaces /
[ M.Talagrand ] / Publ.Math.IHES.   DOI
12 An upper bound on the expected cost of an optimal assignment /
[ R.M.Karp ] / Discrete Algorithms and Complexity: Proceedings of the Japan-U.S.joint seminar