Finding optimal mentor-mentee matches: A case study in applied two-sided matching

Two-Sided Matching is a well-established approach to find allocations and matchings based on the participants' preferences. While its most prominent applications are College Admissions and School Choice problems, this paper applies the concept to the matching of mentors to mentees in a higher education context. Both mentors and mentees have preferences with whom they ideally want to be matched, as well as who they want to avoid. As the general formulation for these types of preferences is NP-hard, several existing approximation algorithms and heuristics are compared with respect to their ability to find a matching with desirable properties. The results show that a combination of evolutionary heuristics and local search approaches works best in finding high-quality solutions, allowing us to find mentor-mentee pairs which are close to the respective ideal match.

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

[2]  Lars Ehlers,et al.  Truncation Strategies in Matching Markets , 2008, Math. Oper. Res..

[3]  Peter Coles,et al.  Optimal Truncation in Matching Markets , 2013, Games Econ. Behav..

[4]  M HalldórssonMagnús,et al.  Improved approximation results for the stable marriage problem , 2007 .

[5]  Jan Kees Winters.  Two-sided matching, a study in game-theoretic modeling and analysis : A.E. Roth and M.A. Oliveira Sotomayor, Econometric Society Monographs No. 18 (Cambridge University Press, Cambridge, 1990) pp. 265, ISBN 0-521-39015-X (hbk), $54.50 , 1992 .

[6]  Katarzyna E. Paluch.  Faster and Simpler Approximation of Stable Matchings , 2014, Algorithms.

[7]  J. Gabszewicz,et al.  On Gale and Shapley "college admissions and the stability of marriage" , 2012 .

[8]  Magnús M. Halldórsson,et al.  Improved approximation results for the stable marriage problem , 2007, TALG.

[9]  M. Bennis,et al.  Caching Meets Millimeter Wave Communications for Enhanced Mobility Management in 5G Networks , 2017, IEEE Transactions on Wireless Communications.

[10]  Marco E. Castillo,et al.  Truncation strategies in two-sided matching markets: Theory and experiment , 2016, Games Econ. Behav..

[11]  Alvin E. Roth.  Deferred acceptance algorithms: history, theory, practice, and open questions , 2008, Int. J. Game Theory.

[12]  Toby Walsh,et al.  Local Search Approaches in Stable Matching Problems , 2013, Algorithms.

[13]  C. Haas.  Incentives and Two-Sided Matching - Engineering Coordination Mechanisms for Social Clouds , 2014 .

[14]  Robert W. Irving,et al.  An efficient algorithm for the “optimal” stable marriage , 1987, JACM.

[15]  Atila Abdulkadiroglu,et al.  School Choice: A Mechanism Design Approach , 2003 .

[16]  Eric McDermid.  A 3/2-Approximation Algorithm for General Stable Marriage , 2009, ICALP.

[17]  Steven Orla Kimbrough,et al.  On heuristics for two-sided matching: revisiting the stable marriage problem as a multiobjective problem , 2010, GECCO '10.

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

[19]  Christian Haas,et al.  Preference-Based Resource Allocation: Using Heuristics to Solve Two-Sided Matching Problems with Indifferences , 2013, GECON.

[20]  Walid Saad,et al.  Context-Aware Small Cell Networks: How Social Metrics Improve Wireless Resource Allocation , 2015, IEEE Transactions on Wireless Communications.

[21]  Shuichi Miyazaki,et al.  Approximation algorithms for the sex-equal stable marriage problem , 2007, TALG.

[22]  David Manlove,et al.  Hard variants of stable marriage , 2002, Theor. Comput. Sci..

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

[24]  Shuichi Miyazaki,et al.  Approximation Algorithms for the Sex-Equal Stable Marriage Problem , 2007, WADS.

[25]  Aytek Erdil,et al.  Two-sided matching with indifferences , 2017, J. Econ. Theory.

[26]  David Manlove,et al.  Approximability results for stable marriage problems with ties , 2003, Theor. Comput. Sci..

[27]  Parag A. Pathak,et al.  Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match , 2009 .

[28]  Donald E. Knuth,et al.  Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms , 1996 .

[29]  Alvin E. Roth,et al.  The Economics of Matching: Stability and Incentives , 1982, Math. Oper. Res..

[30]  Ngo Anh Vien,et al.  Multiobjective Fitness Functions for Stable Marriage Problem using Genetic Algrithm , 2006, 2006 SICE-ICASE International Joint Conference.

[31]  U. Rothblum,et al.  Truncation Strategies in Matching Markets-in Search of Advice for Participants , 1999 .

[32]  Zoltán Király.  Better and Simpler Approximation Algorithms for the Stable Marriage Problem , 2009, Algorithmica.