Kernelization Algorithms for the Vertex Cover Problem: Theory and Experiments

A variety of efficient kernelization strategies for the classic vertex cover problem are developed, implemented and compared experimentally. A new technique, termed crown reduction, is introduced and analyzed. Applications to computational biology are discussed.

[1]  Michael R. Fellows,et al.  Nonconstructive tools for proving polynomial-time decidability , 1988, JACM.

[2]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[3]  Judy Goldsmith,et al.  Nondeterminism Within P , 1993, SIAM J. Comput..

[4]  Michael R. Fellows,et al.  On search decision and the efficiency of polynomial-time algorithms , 1989, STOC '89.

[5]  Abu Khzam,et al.  Topics in Graph Algorithms: Structural Results and Algorithmic Techniques, with Applications , 2003 .

[6]  E. A. Dinic.  Algorithm for solution of a problem of maximal flow in a network with power estimation , 1970 .

[7]  Faisal N. Abu-Khzam,et al.  Scalable parallel algorithms for difficult combinatorial problems: A case study in optimization , 2004, Parallel and Distributed Computing and Networks.

[8]  Faisal N. Abu-khzam,et al.  Topics in Graph Algorithms: Structural Results and Algorithmic Techniques , 2003 .

[9]  Ulrike Stege,et al.  Solving large FPT problems on coarse-grained parallel machines , 2003, J. Comput. Syst. Sci..

[10]  Leslie E. Trotter,et al.  Vertex packings: Structural properties and algorithms , 1975, Math. Program..

[11]  Samir Khuller,et al.  Algorithms column: the vertex cover problem , 2002, SIGA.

[12]  Samir Khuller.  The vertex cover problem , 2002 .

[13]  Weijia Jia,et al.  Vertex Cover: Further Observations and Further Improvements , 2001, J. Algorithms.

[14]  Michael R. Fellows,et al.  On search, decision, and the efficiency of polynomial-time algorithms , 1994, FOCS 1994.

[15]  N. S. Barnett,et al.  Private communication , 1969 .

[16]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .