A Min-Max Theorem on Feedback Vertex Sets

Authors:
Mao-Cheng Cai;Xiaotie Deng;Wenan Zang
Affiliations:
-;-;-
Venue:
Mathematics of Operations Research
Year:
2002

Citing 0
Cited 18

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Linear Programming Based Approximation Algorithms for Feedback Set Problems in Bipartite Tournaments

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Fixed-parameter tractability results for feedback set problems in tournaments

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Linear programming based approximation algorithms for feedback set problems in bipartite tournaments

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Two hardness results on feedback vertex sets

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Tractable feedback vertex sets in restricted bipartite graphs

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Fixed-parameter tractability results for feedback set problems in tournaments

CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
An efficient algorithm for finding maximum cycle packings in reducible flow graphs

ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A polynomial kernel for feedback arc set on bipartite tournaments

ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Fixed-parameter complexity of feedback vertex set in bipartite tournaments

ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Fixed-parameter tractability for the subset feedback set problem and the S-cycle packing problem

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Improved approximation algorithm for the feedback set problem in a bipartite tournament

Operations Research Letters
A quadratic vertex kernel for feedback arc set in bipartite tournaments

MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Feedback vertex sets on restricted bipartite graphs

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A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments

Theory of Computing Systems

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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, whereH is the cycle-vertex incidence matrix ande 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 isNP-complete and approximable within 3.5 based on the min-max theorem.