Instability in Stable Marriage Problem: Matching Unequally Numbered Men and Women. (5th September 2018)

• Record Type: Journal Article
• Authors: Shi, Gui-Yuan; Kong, Yi-Xiu; Chen, Bo-Lun; Yuan, Guang-Hui; Wu, Rui-Jie
• Other Names: Tessone Claudio Academic Editor.
• Is Part Of: Complexity. Volume 2018(2018)
• Publication Date: 2018-09-05
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2018/7409397
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : The goal of the stable marriage problem is to match by pair two sets composed by the same number of elements. Due to its widespread applications in the real world, especially the unique importance to the centralized matchmaker, a very large number of questions have been extensively studied in this field. This article considers a generalized form of the stable marriage problem, where different numbers of men and women need to be matched pairwise and the emergence of single men or women is inevitable. Theoretical analysis and numerical simulations confirm that even a small deviation on the number of men and women from the equality condition can have a large impact on the matching solution of the Gale-Shapley algorithm. These results provide insights to many of the real-world applications when matching two sides with an unequal number.