Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2002.04.01
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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>.

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References

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