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http://dx.doi.org/10.7236/JIIBC.2018.18.4.177

Canonical Latin Square Algorithm for Round-Robin Home-and-Away Sports Leagues Scheduling  

Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
Publication Information
The Journal of the Institute of Internet, Broadcasting and Communication / v.18, no.4, 2018 , pp. 177-182 More about this Journal
Abstract
The home-and-way round-robin sports leagues scheduling problem with minimum brake is very hard to solve in polynomial time. This problem is NP-hard, the complexity status is not yet determined. This paper suggests round-robin sports leagues scheduling algorithm not computer-aided program but by hand with O(n) time complexity for arbitrary number of teams n with always same pattern. The algorithm makes a list of mathes using $n{\times}n$ canonical latin square for n=even teams. Then trying to get home(H) and away(A) with n-2 minimum number of brakes. Also, we get the n=odd scheduling with none brakes delete a team own maximum number of brakes from n=even scheduling.
Keywords
sports leagues scheduling; round-robin; home-and-away; brake; canonical latin square;
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1 R. M. R. Lewis, "A Guide to Graph Colouring Algorithms and Applications: Chapter 7. Designing Sports Leagues," Springer, pp. 169-193, Oct. 2015, ISBN 978-3-319-25728-0, doi:10.1007/978-3-319-25730-3
2 R. V. Rasmussen and M. A. Trick, "Round Robin Scheduling - A Survey," European Journal of Operational Research, Vol. 188, No. 3, pp. 617-636, Aug. 2008, doi:10.1016/j.ejor.2007.05.046   DOI
3 T. Kirkman, "On a Problem in Combinations," Cambridge Dublin Math Journal, Vol. 2, pp. 191-204, 1847.
4 D. de Werra, "Some Models of Graphs for Scheduling Sports Competitions," Discrete Applied Mathematics, Vol. 21, No. 1, pp. 47-65, Sep. 1988, doi:10.1016/0166-218X(88)90033-9   DOI
5 R. Miyashiro and T. Matsui, "A Polynomial-time Algorithm to Find an Equitable Home-Away Assignment," Operational Research Letters, Vol. 33, No. 3, pp. 235-241, May 2005, doi:10.1016/j.orl.2004.06.004   DOI
6 T. Rutjanisarakul and T. Jiarasuksakun, "A Sport Tournament Scheduling by Genetic Algorithm with Swing Method," Cornell University Library, pp. 1-7, arXiv:1704.04879, Apr. 2017.
7 J. P. Hamiez and J. K. Hao, "Solving the Sports League Scheduling Problem with Tabu Search," Workshop on Local Search for Planning and Scheduling, pp. 24-36, Aug. 2000, doi:10.1007/3-540-45612-0_2   DOI
8 S. B. Choi, S. S. Jeung, and T. Y. Han, "Home-Away Sports League Scheduling with Minimum Breaks," Journal of Korean Society of Sports Science, Vol. 24, No. 4, pp. 691-701, Aug. 2015, uci:G704-001369.2015.24.4.098
9 J. P. Hamiez and J. K. Hao, "A Linear-time Algorithm to Solve the Sports League Scheduling Problem(prob026 of CSPLib)," Discrete Applied Mathematics, Vol. 143, No. 1-3, pp. 252-265, Sep. 2004, doi:10.1016/j.dam.2003.10.009   DOI
10 M. Elf, M. Junger, and G. Rinaldi, "Minimizing Breaks by Maximizing Cuts," Operational Research Letters, Vol. 31, No. 5, pp. 343-349, Sep. 2003, doi:10.1016/S0167-6377(03)00025-7   DOI
11 M. X. Goemans and D. P. Williamson, "Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems using Semidefinite Programming," Journal of ACM, Vol. 42, No. 6, pp. 1115-1145, Nov. 1995, doi:10.1145/227683.227684   DOI
12 W. D. Wallis and J. C. George, "Introduction to Combinatorics," CRC Press, p. 212, 2011, ISBN 978-1-4398-0623-4
13 R. Miyashiro and T. Matsui, "Semidefinite Programming based Approaches to the Break Minimization Problem," Computers & Operations Research, Vol. 33, No. 7, pp. 1975-1982, Jul. 2006, doi:10.1016/j.cor.2004.09.030   DOI
14 M. A. Trick, "A Schedule-then-Break Approach to Sports Timetabling," International Conference on the Practice and Theory of Automated Timetabling III, pp. 242-253, 2000.