A min-max theorem on feedback vertex sets

• 成果类型: Article
• 署名作者: Cai, MC; Deng, XT; Zang, WN
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; City University of Hong Kong; University of Hong Kong
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.27.2.361.328
• 发表日期: 2002
• 页码: 361-371

摘要

We establish a necessary and sufficient condition for the linear system {x : Hx greater than or equal to e, x greater than or equal to 0} associated with a bipartite tournament to be totally dual integral, where H is the cycle-vertex incidence matrix and e is the all-one vector. The consequence is a min-max relation on packing and covering cycles, together with strongly polynomial time algorithms for the feedback vertex set problem and the cycle packing problem on the corresponding bipartite tournaments. In addition, we show that the feedback vertex set problem on general bipartite tournaments is NP-complete and approximable within 3.5 based on the min-max theorem.