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A Min-Max Theorem on Feedback Vertex Sets

Mao-Cheng Cai, Xiaotie Deng and Wenan Zang
Mathematics of Operations Research
Vol. 27, No. 2 (May, 2002), pp. 361-371
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3690594
Page Count: 11
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A Min-Max Theorem on Feedback Vertex Sets
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Abstract

We establish a necessary and sufficient condition for the linear system {x: Hx ≥ e,x ≥ 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.

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