A branch and bound algorithm for the stability number of a sparse graph

INFORMS Journal on Computing

Volumn 10, Issue 4, 1998, Pages 438-447

  Sewell, E C ^a  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

Author keywords

Branch and bound; Matchings; Maximum stable sets; Networks graphs; Programming

Indexed keywords

EID: 0342771718     PISSN: 10919856     EISSN: None     Source Type: Journal    
DOI: 10.1287/ijoc.10.4.438     Document Type: Article

References (29)

1. S. ARORA and S. SAFRA, 1992. Probabilistic Checking of Proofs: A New Characterization of NP, in Proceedings of the 33rd IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 2-13.
2. L. BABEL, 1991. Finding Maximum Cliques in Arbitrary and in Special Graphs, Computing 46, 321-341.
3. L. BABEL and G. TINHOFER, 1990. A Branch and Bound Algorithm for the Maximum Clique Problem, ZOR-Methods and Models of Operations Research 34, 207-217.
4. E. BALAS and C.S. YU, 1986. Finding a Maximum Clique in an Arbitrary Graph, SIAM Journal on Computing 15:4, 1054-1068.
5. J.M. BOURJOLLY, P. GILL, G. LAPORTE, and H. MERCURE, 1996. An Exact Quadratic 0-1 Algorithm for the Stable Set Problem, in DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 26: Cliques, Coloring, and Satisfiability, D.S. Johnson and M.A. Trick (eds.), American Mathematical Society, Providence, RI, 53-73.
6. J.-M. BOURJOLLY and W.R. PULLEYBLANK, 1989. König-Egerváry Graphs, 2-Bicritical Graphs and Fractional Matchings, Discrete Applied Mathematics 24, 63-82.
7. D. BRÉLAZ, 1979. New Methods to Color the Vertices of a Graph, Communications of the ACM 22, 251-256.
8. M. BROCKINGTON and J.C. CULBERSON, 1996. Camouflaging Independent Sets in Quasi-Random Graphs, in DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 26: Cliques, Coloring, and Satisfiability, D.S. Johnson and M.A. Trick (eds.), American Mathematical Society, Providence, RI, 75-88.
9. R. CARRAGHAN and P.M. PARDALOS, 1990. An Exact Algorithm for the Maximum Clique Problem, Operations Research Letters 9, 375-382.
10. R.W. DEMING, 1979. Independence Numbers of Graphs - An Extension of the König-Egerváry Theorem, Discrete Mathematics 27, 23-33.
11. U. FEIGE, S. GOLDWASSER, L. LOVÁSZ, S. SAFRA, and M. SZEGEDY, 1991. Approximating Clique is Almost NP-Complete, in Proceedings of the 32rd IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 2-12.
12. C. FRIDEN, A. HERTZ, and D. DE WERRA, 1989. STABULUS: A Technique for Finding Stable Sets in Large Graphs with Tabu Search, Computing 42, 35-44.
13. C. FRIDEN, A. HERTZ, and D. DE WERRA, 1990. TABARIS: An Exact Algorithm Based on Tabu Search for Finding a Maximum Independent Set in a Graph, Computers and Operations Research 17:5, 437-445.
14. D.R. FULKERSON, G.L. NEMHAUSER, and L.E. TROTTER, JR., 1974. Two Computationally Difficult Set Covering Problems that Arise in Computing the 1-Width of Incidence Matrices of Steiner Triple Systems, Mathematical Programming Study 2, 72-81.
15. T. GALLAI, 1959. Über extreme Punkt- und Kantenmengen, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominantae Sectio Mathematica 2, 133-138.
16. M. GENDREAU, P. SORIANO, and L. SALVAIL, 1993. Solving the Maximum Clique Problem using a Tabu Search Approach, Annals of Operations Research 41, 385-403.
17. G.R. GRIMMETT and W.R. PULLEYBLANK, 1985. Random NearRegular Graphs and the Node Packing Problem, Operations Research Letters 4, 169-174.
18. P.L. HAMMER, P. HANSEN, and B. SIMEONE, 1982. Vertices Belonging to All or to No Maximum Stable Sets of a Graph, SIAM Journal on Algebraic and Discrete Methods 3:4, 511-522.
19. D.S. JOHNSON, C.R. ARAGON, L.A. MCGEOCH, and C. SCHEVON, 1991. Optimization by Simulated Annealing: An Experimental Evaluation. Part II, Graph Coloring and Number Partitioning, Operations Research 39:3, 378-406.
20. C. MANNINO and A. SASSANO, 1994. An Exact Algorithm for the Maximum Stable Set Problem, Journal of Combinatorial Optimization and Applications 3, 243-258.
21. G.L. NEMHAUSER and G. SIGISMONDI, 1992. A Strong Cutting Plane/Branch-and-Bound Algorithm for Node Packing, Journal of the Operational Research Society 43:5, 443-457.
22. G.L. NEMHAUSER and L.E. TROTTER, JR., 1974. Properties of Vertex Packing and Independence System Polyhedra, Mathematical Programming 6, 48-61.
23. G.L. NEMHAUSER and L.E. TROTTER, JR., 1975. Vertex Packings: Structural Properties and Algorithms, Mathematical Programming 8, 232-248.
24. M.W. PADBERG, 1973. On the Facial Structure of Set Packing Polyhedra, Mathematical Programming 5, 199-215.
25. P.M. PARDALOS and G.P. RODGERS, 1992. A Branch and Bound Algorithm for the Maximum Clique Problem, Computers and Operations Research 19, 363-375.
26. L.A. SANCHIS and A. JAGOTA, 1996. Some Experimental and Theoretical Results on Test Case Generators for the Maximum Clique Problem, INFORMS Journal on Computing 8:2, 87-102.
27. F. STERBOUL, 1979. A Characterization of the Graphs in Which the Transversal Number Equals the Matching Number, Journal of Combinatorial Theory, Series B 27, 228-229.
28. D.J.A. WELSH and M.B. POWELL, 1967. An Upper Bound for the Chromatic Number of a Graph and Its Application to Timetabling Problem, The Computer Journal 10, 85-86.
29. J. XUE, 1991. Fast Algorithms for Vertex Packing and Related Problems, PhD thesis, Carnegie Mellon University, Pittsburgh, PA.