The Journal of the Institute of Internet, Broadcasting and Communication (한국인터넷방송통신학회논문지)

The Institute of Internet, Broadcasting and Communication (한국인터넷방송통신학회)
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Canonical Latin Square Algorithm for Round-Robin Home-and-Away Sports Leagues Scheduling

라운드-로빈 홈 앤드 어웨이 스포츠 리그 대진표 작성 정규형 라틴 방진 알고리즘

  • Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
  • 이상운 (강릉원주대학교 과학기술대학 멀티미디어공학과)
  • Received : 2018.05.20
  • Accepted : 2018.08.10
  • Published : 2018.08.31
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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.

최소 제동 수를 갖는 홈 앤드 어웨이 라운드-로빈 경기일정 대진표를 작성하는 문제는 매우 어려워 NP-난제로 알려져 있다. 본 논문에서는 임의의 팀 수 n에 대해서도 항상 동일한 패턴으로 경기일정 대진표를 O(n) 수행 복잡도로 컴퓨터 프로그램 도움 없이 직접 손으로 작성할 수 있는 알고리즘을 제안하였다. 제안된 알고리즘은 n=even 팀에 대해 $n{\times}n$ 정규형 라틴 방진을 작성하여 대진표를 작성하고, 최소 제동 수가 n-2 가 되도록 홈-어웨이를 배정하였다. 또한, n=odd에 대해서는 n=even 결과에서 최대 제동 수를 갖는 n번째 팀을 삭제하는 방법으로 제동이 전혀 없는 대진표를 작성하였다.

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