Random Assignment with Integer Costs

Abstract

The random assignment problem is to minimize the cost of an assignment in a n × n matrix of random costs. In this paper we study this problem for some integer valued cost distributions. We consider both uniform distributions on 1, 2,. .. , m, for m = n or n 2 , and random permutations of 1, 2,. .. , n for each row, or of 1, 2,. .. , n 2 for the whole matrix. We find the limit of the expected cost for the "n 2 " cases, and prove bounds for the "n" cases. This is done by simple coupling arguments together with Aldous recent results for the continuous case. We also present a simulation study of these cases.

Random assignment problems

“…An immediate benefit of such an assumption is that all feasible solutions can be considered to have (almost surely) different costs. An interesting departure from this general setup is found in the paper by Parviainen (2004), where an LAP with discretely distributed random assignment costs is discussed. Making use of some of the results of Aldous (2001), Parviainen considers the following cases of random LAP (1):…”

“…Then, Parviainen (2004) shows that the limiting expected optimal value E½L ðÁÞ ¼ lim n!1 E½L ðÁÞ n of the random LAP with the described above structure of the cost matrix satisfies:…”

Constructing Minimal Perfect Hash Functions Using SAT Technology

“…M is also the bijective mapping of the MPHF being built. Since G fits Parviainen's proposed "Case II" (Parviainen 2004), M has weight approximately 1.83n, asymptotically, which was determined experimentally.…”

Uncertain random assignment problem

“…Buck et al [17] conjecture an explicit formula for the expected value of the random k-assignment. Parviainen [18] discusses an assignment problem with discrete random costs. Li et al [19] present a new genetic algorithm selection scheme to solve the random assignment problem.…”

“…Assumption(coefficient) Mathematical model deterministic model [1][2][3][4][5][6][7][8][9][10][11][12] constant integer programming random model [13][14][15][16][17][18][19][20][21] independent random variable stochastic programming uncertain model [27] independent uncertain variable uncertain programming our model independent uncertain variable and independent random variable uncertain random programming…”