Semidefinite programming based approaches to home-away assignment problems in sports scheduling

Authors:
Ayami Suzuka;Ryuhei Miyashiro;Akiko Yoshise;Tomomi Matsui
Affiliations:
Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan;Institute of Symbiotic Science and Technology, Tokyo University of Agriculture and Technology, Koganei, Tokyo, Japan;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan;Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo, Japan
Venue:
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Year:
2005

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Abstract

For a given schedule of a round-robin tournament and a matrix of distances between homes of teams, an optimal home-away assignment problem is to find a home-away assignment that minimizes the total traveling distance. We propose a technique to transform the problem to MIN RES CUT . We apply Goemans and Williamson's 0.878-approximation algorithm for MAX RES CUT, which is based on a positive semidefinite programming relaxation,to the obtained MIN RES CUT instances. Computational experiments show that our approach quickly generates solutions of good approximation ratios.