대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제17권2호
  • /
  • Pages.321-330
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  • 2002
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 발행 : 2002.04.01
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초록

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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참고문헌

  1. Probab.Theory Relat.Fields v.93 Asymptotics in the random assignment problem D.J.Aldous https://doi.org/10.1007/BF01192719
  2. Random Struct.Alg. The ?(2) limit in the random assignment problem
  3. 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
  4. Proceedings of SODA The probabilistic relationship between the assignment and asymmetric traveling salesman problems A.M.Frieze;G.B.Sorkin
  5. Math.Oper.Res. v.18 A Lower bound on the expected cost of an optimal assignemnt M.X.Goemans;M.S.Kodiallam https://doi.org/10.1287/moor.18.2.267
  6. Discrete Algorithms and Complexity: Proceedings of the Japan-U.S.joint seminar An upper bound on the expected cost of an optimal assignment R.M.Karp
  7. The Traveling Salesman Problem Probabilistic analysis of heuristics R.M.Karp;J.M.Steele
  8. B.A.thesis, Department of Mathematics, Princeton University The assignment problem with uniform (0, 1) cost matrix A.J.Lazarus
  9. Ph.D.thesis, Kungl Tekniska Hogskolan Asymptotic properties of random assignment problems B.Olin
  10. Probability Theory and Combinatorial Optimization J.M.Steele
  11. Publ.Math.IHES. v.81 Concentration of measure and isoperimetric inequalities in product spaces M.Talagrand https://doi.org/10.1007/BF02699376
  12. SIAM J.Comput. v.8 On the expected value of a random assignment problem D.W.Walkup https://doi.org/10.1137/0208036