ournal of Statistical Mechanics : J Theory and Experiment Stable roommates problem with random preferences

The stable roommates problem with n agents has worst case complexity O(n 2 ) in time and space. Random instances can be solved faster and with less memory, however. We introduce an algorithm that has average time and space complexity O(n 3 2) for random instances. We use this algorithm to simulate large instances of the stable roommates problem and to measure the probabilty pn that a random instance of size n admits a stable matching. Our data support the conjecture that pn = !( n ! 1/4 ).

[1]  Stephan Mertens,et al.  Small random instances of the stable roommates problem , 2015, 1502.06635.

[2]  Stephan Mertens,et al.  Random stable matchings , 2005 .

[3]  David Manlove,et al.  Algorithmics of Matching Under Preferences , 2013, Bull. EATCS.

[4]  Robert W. Irving,et al.  The Stable marriage problem - structure and algorithms , 1989, Foundations of computing series.

[5]  T. Nieuwenhuizen.  The marriage problem and the fate of bachelors , 1997, cond-mat/9710077.

[6]  Michael Dzierzawa,et al.  Statistics of stable marriages , 2000 .

[7]  M. Marsili,et al.  Scaling behavior in the stable marriage problem , 1997 .

[8]  Jimmy J. M. Tan.  A Necessary and Sufficient Condition for the Existence of a Complete Stable Matching , 1991, J. Algorithms.

[9]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[10]  Roberto Mulet,et al.  The marriage problem: From the bar of appointments to the agency , 2006 .

[11]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[12]  Robert W. Irving,et al.  An Upper Bound for the Solvability of a Random Stable Roommates Instance , 1994, Random Struct. Algorithms.

[13]  R. Italy,et al.  Beauty and distance in the stable marriage problem , 2000, cond-mat/0008337.

[14]  Robert W. Irving.  An Efficient Algorithm for the "Stable Roommates" Problem , 1985, J. Algorithms.

[15]  Boris Pittel,et al.  The stable roommates' problem with random preferences , 1993 .

[16]  Cristopher Moore,et al.  The Nature of Computation , 2011 .