An Approximation Algorithm for the Bipartite Traveling Tournament Problem

• 成果类型: Article
• 署名作者: Hoshino, Richard; Kawarabayashi, Ken-ichi
• 署名单位: Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan; Japan Science & Technology Agency (JST)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2013.0597
• 发表日期: 2013
• 页码: 720-728

摘要

The bipartite traveling tournament problem (BTTP) is an NP-complete scheduling problem whose solution is a double round-robin inter-league tournament with minimum total travel distance. The 2n-team BTTP is a variant of the well-known traveling salesman problem (TSP), albeit much harder as it involves the simultaneous coordination of 2n teams playing a sequence of home and away games under fixed constraints, rather than a single entity passing through the locations corresponding to the teams' home venues. As the BTTP requires a distance-optimal schedule linking venues in close proximity, we provide an approximation algorithm for the BTTP based on an approximate solution to the corresponding TSP. We prove that our polynomial-time algorithm generates a 2n-team inter-league tournament schedule whose total distance is at most 1 + 2c/3 + (3 c)/(3n) times the total distance of the optimal BTTP solution, where c is the approximation factor of the TSP. In practice, the actual approximation factor is far better; we provide a specific example by generating a nearly-optimal inter-league tournament for the 30-team National Basketball Association, with total travel distance just 1.06 times the trivial theoretical lower bound.