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ON THE RANDOM n×n ASSIGNMENT PROBLEM

  • Lee, Sung-Chul (Department of Mathematics, Yonsei University) ;
  • Zhonggen, Su (Department of Mathematics, Zhejiang University and Department of Mathematics, Yonsei University)
  • Published : 2002.10.01

Abstract

Consider the random n $\times$ m assignment problem with m $\geq$ $_{i,j}$ Let $u_{i,j}$ be iid uniform random variables on [0, 1] and exponential random variables with mean 1, respectively, and let $U_{n, m}$ and $T_{n, m}$ denote the optimal assignment costs corresponding to $u_{i, j}$ and $t_{i, j}$. In this paper we first give a comparison result about the discrepancy E $T_{n, m}$ -E $U_{n, m}$. Using this comparison result with a known lower bound for Var( $T_{n, m}$) we obtains a lower bound for Var( $U_{n, m}$). Finally, we study the way that E $U_{n, m}$ and E $T_{n, m}$ vary as m does. It turns out that only when m - n is large enough, the cost decreases significantly.tly.

Keywords

n${\times}$m assignment problem;bipartite matching;optimal assignment

References

  1. Random Struct. Alg., to appear The ?(2) limit in the random assignment problem
  2. Preprint An assignment problem at high temperature
  3. Comm. Korean Math. Soc., to appear On the fluctuation in the random assignment problem Lee S.;Su Z. https://doi.org/10.4134/CKMS.2002.17.2.321
  4. Proceedings of SODA The probabilistic relationship between the as-signment and asymmetric traveling salesman problems A.M. Frieze;G.B. Sorkin
  5. Random Struct. Alg v.15 Constructive bounds and exact expectations for the random assignment problem D. Coppersmith;G.B. Sorkin https://doi.org/10.1002/(SICI)1098-2418(199909)15:2<113::AID-RSA1>3.0.CO;2-S
  6. Probab. Theory Relat. Fields v.93 Asymptotics in the random assignment problem D.J. Aldous https://doi.org/10.1007/BF01192719
  7. Preprint Exact expectations and distributions for the random assignment problem S.E. Alm;G.B. Sorkin
  8. Publ. Math. IHES v.81 Concentration of measure and isoperimetric inequalities in product spaces M. Talagrand https://doi.org/10.1007/BF02699376