A Marriage Problem Using Threshold Algorithm

Title & Authors
A Marriage Problem Using Threshold Algorithm
Lee, Sang-Un;

Abstract
This paper deals with a newly proposed algorithm for stable marriage problem, which I coin threshold algorithm. The proposed algorithm firstly constructs an $\small{n{\times}n}$ matrix of the sum of each sex's preference over the members of the opposite sex. It then selects the minimum value from each row and column to designate the maximum value of the selected as the sum threshold $\small{p^*_{ij}}$. It subsequently deletes the maximum preference $\small{_{mzx}p_{ij}}$ from a matrix derived from deleting $\small{p_{ij}}$ > $\small{p^*_{ij}}$, until $\small{{\mid}c_i{\mid}=1}$ or $\small{{\mid}c_j{\mid}=1}$. Finally, it undergoes an optimization process in which the sum preference is minimized. When tested on 7 stable marriage problems, the proposed algorithm has proved to improve on the existing solutions.
Keywords
Marriage Problem;Matching;Preference;Threshold Value;
Language
Korean
Cited by
References
1.
T. Szabo, "Graph Theory," Institute of Technical Computer Science, Department of Computer Science, ETH, 2004.

2.
M. X. Goemans, "18,433 Combinatorial Operation: Lecture Notes on Bipartite Matching," Massachusetts Institute of Technology, 2007.

3.
J. T. Eyck, 'Algorithm Analysis and Design," http://www.academic.marist.edu/-jzbv/algorithms/TheStableMarriageProblem.htm, 2008.

4.
Wikipedia, "Stable Marriage Problem,," http://en.wikipedia.org/wiki/Stable_marriage_problem,Wikimedia Foundation Inc., 2010.

5.
W. Hunt, "The Stable Marriage Problem," Lane Department of Computer Science and Electrical Engineering, West Virginia University, 2004.

6.
S. U. Lee, "Marriage Problem Algorithm Based on the Most Preferred Rank Selection Method," Journal of IIBC, Vol. 14, No. 3, pp. 111-117, Jun. 2014.

7.
S. U. Lee, "A Marriage Problem Algorithm Based on Duplicated Sum of Inter-Preference Moving Method," Journal of KSCI, Vol. 20, No. 5, pp. 107-112, May 2015.

8.
S. U. Lee, "Marriage Problem Algorithm based on the Maximum Dispreference Sum-Delete Method," Journal of IIBC, Vol. 15, No. 3, pp. 149-154, Jun. 2015.

9.
R. W. Irving, "Stable Matching Problems with Exchange Restrictions," Journal of Combinatorial Optimization, Vol. 16, pp. 344-360, 2008.

10.
R. W. Irving, "The Man-Exchange Stable Marriage Problem," Department of Computing Science, Research Report, TR-2004-177, University of Glasgow, UK., 2004.

11.
K. Iwama, "Stable Matching Problems," http://www.lab2.kuis.kyoto-u.ac.jp/-iwama/papers/isaac2006-3.ppt, 2006.

12.
J. H. Kim, "MAT 2106-02 Discrete Mathematics: Combination Theory within the framework of Marriage Problem," Department of Mathematics, Yousei University, Korea, 2001.

13.
H. W. Kuhn, "50 Years of Integer Programming 1958-2008: From the Early Years to the State-of-the-Art, Chapter 2. The Hungarian Method for the Assignment Problem," Springer-Verlag Berlin Heidelberg, pp 29-47, Nov. 2009.