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Physics > Physics and Society

arXiv:1502.02163 (physics)
[Submitted on 7 Feb 2015]

Title:Analysis of ground state in random bipartite matching

Authors:Gui-Yuan Shi, Yi-Xiu Kong, Hao Liao, Yi-Cheng Zhang
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Abstract:In human society, a lot of social phenomena can be concluded into a mathematical problem called the bipartite matching, one of the most well known model is the marriage problem proposed by Gale and Shapley. In this article, we try to find out some intrinsic properties of the ground state of this model and thus gain more insights and ideas about the matching problem. We apply Kuhn-Munkres Algorithm to find out the numerical ground state solution of the system. The simulation result proves the previous theoretical analysis using replica method. In the result, we also find out the amount of blocking pairs which can be regarded as a representative of the system stability. Furthermore, we discover that the connectivity in the bipartite matching problem has a great impact on the stability of the ground state, and the system will become more unstable if there were more connections between men and women.
Comments: 14 pages,6 figures
Subjects: Physics and Society (physics.soc-ph); Social and Information Networks (cs.SI)
Cite as: arXiv:1502.02163 [physics.soc-ph]
  (or arXiv:1502.02163v1 [physics.soc-ph] for this version)
  https://doi.org/10.48550/arXiv.1502.02163

Submission history

From: Hao Liao [view email]
[v1] Sat, 7 Feb 2015 17:13:00 UTC (87 KB)
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