ON THE FLUCTUATION IN THE RANDOM ASSIGNMENT PROBLEM

Title & Authors
ON THE FLUCTUATION IN THE RANDOM ASSIGNMENT PROBLEM
Lee, Sung-Chul; Su, Zhong-Gen;

Abstract
Consider the random assignment (or bipartite matching) problem with iid uniform edge costs t(i, j). Let $\small{A_{n}}$ be the optimal assignment cost. Just recently does Aldous [2] give a rigorous proof that E $\small{A_{n}}$ longrightarrowζ(2). In this paper we establish the upper and lower bounds for Var $\small{A_{n}}$ , i.e., there exist two strictly positive but finite constants $\small{C_1}$ and $\small{C_2}$ such athat $\small{C_1}$ $\small{n^{(-5}}$2)/ (log n)$\small{^{(-3}}$2)/ $\small{\leq}$ Var $\small{A_{n}}$ $\small{\leq}$ $\small{C_2}$ $\small{n^{-1}}$ (log n)$\small{^2}$.EX>.
Keywords
assignment problem;bipartite matching matching;conditional variance;probabilistic analysis of algorithms;
Language
English
Cited by
1.
ON THE RANDOM n×n ASSIGNMENT PROBLEM,;;

대한수학회논문집, 2002. vol.17. 4, pp.719-729
References
1.
Probab.Theory Relat.Fields, 1992. vol.93. pp.507-534

2.
Random Struct.Alg., 2001.

3.
Random Struct.Alg., 1999. vol.15. pp.113-144

4.
Proceedings of SODA, 2001. pp.652-660

5.
Math.Oper.Res., 1993. vol.18. pp.267-274

6.
Discrete Algorithms and Complexity: Proceedings of the Japan-U.S.joint seminar, 1987. pp.1-4

7.
The Traveling Salesman Problem, 1985. pp.181-205

8.
B.A.thesis, Department of Mathematics, Princeton University, 1979.

9.
Ph.D.thesis, Kungl Tekniska Hogskolan, 1992.

10.
Probability Theory and Combinatorial Optimization, 1997.

11.
Publ.Math.IHES., 1995. vol.81. pp.73-205

12.
SIAM J.Comput., 1979. vol.8. pp.440-442