Solving hard set covering problems

We propose a new branch-and-bound algorithm to solve hard instances of set covering problems arising from Steiner triple systems.

[1]  Gilbert Laporte,et al.  A Combinatorial Column Generation Algorithm for the Maximum Clique and Stable Set Problems , 1994 .

[2]  Gautam Mitra,et al.  Solution of Set-Covering and Set-Partitioning Problems Using Assignment Relaxations , 1992 .

[3]  G. Nemhauser,et al.  A Strong Cutting Plane/Branch-and-Bound Algorithm for Node Packing , 1992 .

[4]  Egon Balas,et al.  A lift-and-project cutting plane algorithm for mixed 0–1 programs , 1993, Math. Program..

[5]  J. Beasley,et al.  Enhancing an algorithm for set covering problems , 1992 .

[6]  Mauricio G. C. Resende,et al.  An interior point algorithm to solve computationally difficult set covering problems , 1991, Math. Program..

[7]  Davis Avis.  A note on some computationally difficult set covering problems , 1980, Math. Program..

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  M. Fisher,et al.  Optimal solution of set covering/partitioning problems using dual heuristics , 1990 .

[10]  D. R. Fulkerson,et al.  Two computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems , 1974 .

[11]  M. Resende,et al.  A probabilistic heuristic for a computationally difficult set covering problem , 1989 .

[12]  Daniel Bausch.  Computational advances in the solution of large-scale covering and set partitioning problems , 1982 .

[13]  Egon Balas,et al.  Finding a Maximum Clique in an Arbitrary Graph , 1986, SIAM J. Comput..

[14]  Andrew C. Ho,et al.  Set covering algorithms using cutting planes, heuristics, and subgradient optimization: A computational study , 1980 .

[15]  Carlo Mannino,et al.  An exact algorithm for the maximum stable set problem , 1994, Comput. Optim. Appl..

[16]  A. Kaufmann,et al.  Methods and models of operations research , 1963 .

[17]  Gottfried Tinhofer,et al.  A branch and bound algorithm for the maximum clique problem , 1990, ZOR Methods Model. Oper. Res..