Minimum clique cover in claw-free perfect graphs and the weak Edmonds-Johnson property

We give new algorithms for the minimum (weighted) clique cover in a claw-free perfect graph G, improving the complexity from O(|V(G)|5) to O(|V(G)|3). The new algorithms build upon neat reformulations of the problem: it basically reduces either to solving a 2-SAT instance (in the unweighted case) or...

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Autor principal: Bonomo, F.
Otros Autores: Oriolo, G., Snels, C., Stauffer, G.
Formato: Acta de conferencia Capítulo de libro
Lenguaje:Inglés
Publicado: 2013
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100 1 |a Bonomo, F. 
245 1 0 |a Minimum clique cover in claw-free perfect graphs and the weak Edmonds-Johnson property 
260 |c 2013 
270 1 0 |m Bonomo, F.; IMAS-CONICET, Departamento de Computación, Universidad de Buenos AiresArgentina; email: fbonomo@dc.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Aspvall, B., Plass, M., Tarjan, R., A linear-time algorithm for testing the truth of certain quantified boolean formulas (1979) Inf. Process. Lett., 8 (3), pp. 121-123 
504 |a Bagnara, R., Hill, P.M., Zaffanella, E., An improved tight closure algorithm for integer octagonal constraints (2008) Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4905 LNCS, pp. 8-21. , DOI 10.1007/978-3-540-78163-9-6, Verification, Model Checking, and Abstract Interpretation - 9th International Conference, VMCAI 2008, Proceedings 
504 |a Berge, C., (1973) Graphs and Hypergraphs, , Dunod, Paris 
504 |a Bonomo, F., Oriolo, G., Snels, C., Minimum Weighted Clique Cover on Strip-Composed Perfect Graphs (2012) LNCS, 7551, pp. 22-33. , Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds.) WG 2012. Springer, Heidelberg 
504 |a Chvátal, V., On certain polytopes associated with graphs (1975) J. Combin. Theory, 18 (2), pp. 138-154. , Ser. B 
504 |a Chvátal, V., Sbihi, N., Recognizing claw-free perfect graphs (1988) J. Combin. Theory, 44, pp. 154-176. , Ser. B 
504 |a Edmonds, J., Johnson, E., Matching: A well-solved class of integer linear programs (1970) Combinatorial Structures and Their Applications, pp. 89-92. , Guy, R., Hanani, H., Sauer, N., Schönheim, J. (eds.) Gordon and Breach, New York 
504 |a Edmonds, J., Johnson, E., Matching, Euler tours and the Chinese postman (1973) Math. Program., 5, pp. 88-124 
504 |a Faenza, Y., Oriolo, G., Stauffer, G., An algorithmic decomposition of claw-free graphs leading to an O (n 3)-algorithm for the weighted stable set problem (2011) Proc. 22nd SODA, San Francisco, CA, pp. 630-646. , Randall, D. (ed.) 
504 |a Fulkerson, D., On the perfect graph theorem (1973) Mathematical Programming, pp. 69-76. , Hu, T., Robinson, S. (eds.) Academic Press, New York 
504 |a Gerards, A., Schrijver, A., Matrices with the Edmonds-Johnson property (1986) Combinatorica, 6 (4), pp. 365-379 
504 |a Grötschel, M., Lovász, L., Schrijver, A., (1988) Geometric Algorithms and Combinatorial Optimization, , Springer, Berlin 
504 |a Harvey, W., Stuckey, P., A unit two variable per inequality integer constraint solver for constraint logic programming (1997) The 20th Australasian Computer Science Conference, Sydney, Australia, pp. 102-111. , Australian Computer Science Communications 
504 |a Hsu, W., Nemhauser, G., Algorithms for minimum covering by cliques and maximum clique in claw-free perfect graphs (1981) Discrete Math., 37, pp. 181-191 
504 |a Hsu, W., Nemhauser, G., A polynomial algorithm for the minimum weighted clique cover problem on claw-free perfect graphs (1982) Discrete Math., 38 (1), pp. 65-71 
504 |a Jaffar, J., Maher, M.J., Stuckey, P.J., Yap, R.H.C., Beyond Finite Domains (1994) LNCS, 874, pp. 86-94. , PPCP 1994. Springer, Heidelberg 
504 |a Korte, B., Vygen, J., (2011) Combinatorial Optimization: Theory and Algorithms, , Springer, Berlin 
504 |a Lahiri, S.K., Musuvathi, M., An Efficient Decision Procedure for UTVPI Constraints (2005) LNCS (LNAI), 3717, pp. 168-183. , Gramlich, B. (ed.) FroCos 2005. Springer, Heidelberg 
504 |a Maffray, F., Reed, B., A description of claw-free perfect graphs (1999) J. Combin. Theory, 75 (1), pp. 134-156. , Ser. B 
504 |a Padberg, M., Perfect zero-one matrices (1974) Math. Program., 6, pp. 180-196 
504 |a Peis, B., (2007) Structure Analysis of Some Generalizations of Matchings and Matroids under Algorithmic Aspects, , PhD thesis, Universität zu Köln 
504 |a Schrijver, A., Disjoint homotopic paths and trees in a planar graph (1991) Discrete Comput. Geom., 6 (1), pp. 527-574 
504 |a Schrijver, A., Combinatorial Optimization. Polyhedra and Efficiency (2003) Algorithms and Combinatorics, 24. , 3 volumes. Springer, Berlin 
504 |a Schutt, A., Stuckey, P., Incremental satisfiability and implication for UTVPI constraints (2010) INFORMS J. Comput., 22 (4), pp. 514-527 
504 |a Seshia, S., Subramani, K., Bryant, R., On solving Boolean combinations of UTVPI constraints (2007) J. Satisf. Boolean Model. Comput., 3, pp. 67-90 
504 |a Tarjan, R., Depth-first search and linear graph algorithms (1972) SIAM J. Comput., 1 (2), pp. 146-160 
504 |a Whitesides, S., A method for solving certain graph recognition and optimization problems, with applications to perfect graphs (1984) North-Holland Mathematics Studies, 88, pp. 281-297. , Berge, C., Chvátal, V. (eds.) Topics on Perfect Graphs, North-HollandA4 - Mathematical Optimization Society 
520 3 |a We give new algorithms for the minimum (weighted) clique cover in a claw-free perfect graph G, improving the complexity from O(|V(G)|5) to O(|V(G)|3). The new algorithms build upon neat reformulations of the problem: it basically reduces either to solving a 2-SAT instance (in the unweighted case) or to testing if a polyhedra associated with the edge-vertex incidence matrix of a bidirected graph has an integer solution (in the weighted case). The latter question was elegantly answered using neat polyhedral arguments by Schrijver in 1994. We give an alternative approach to this question combining pure combinatorial arguments (using techniques from 2-SAT and shortest paths) with polyhedral ones. Our approach is inspired by an algorithm from the Constraint Logic Programming community and we give as a side benefit a formal proof that the corresponding algorithm is correct (apparently answering an open question in this community). Interestingly, the systems we study have properties closely connected with the so-called Edmonds-Johnson property and we study some interesting related questions. © 2013 Springer-Verlag.  |l eng 
593 |a IMAS-CONICET, Departamento de Computación, Universidad de Buenos Aires, Argentina 
593 |a Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università Tor Vergata, Roma, Italy 
593 |a Bordeaux Institute of Mathematics, France 
690 1 0 |a BIDIRECTED GRAPHS 
690 1 0 |a CLAW-FREE PERFECT GRAPHS 
690 1 0 |a CLIQUE COVER 
690 1 0 |a EDMONDS-JOHNSON PROPERTY 
690 1 0 |a ALTERNATIVE APPROACH 
690 1 0 |a BIDIRECTED GRAPH 
690 1 0 |a CLIQUE COVER 
690 1 0 |a CONSTRAINT LOGIC PROGRAMMING 
690 1 0 |a EDMONDS-JOHNSON PROPERTY 
690 1 0 |a INCIDENCE MATRICES 
690 1 0 |a INTEGER SOLUTIONS 
690 1 0 |a PERFECT GRAPH 
690 1 0 |a ALGORITHMS 
690 1 0 |a COMBINATORIAL OPTIMIZATION 
690 1 0 |a INTEGER PROGRAMMING 
690 1 0 |a LOGIC PROGRAMMING 
690 1 0 |a GRAPH THEORY 
700 1 |a Oriolo, G. 
700 1 |a Snels, C. 
700 1 |a Stauffer, G. 
711 2 |c Valparaiso  |d 18 March 2013 through 20 March 2013  |g Código de la conferencia: 96207 
773 0 |d 2013  |g v. 7801 LNCS  |h pp. 86-97  |p Lect. Notes Comput. Sci.  |n Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)  |x 03029743  |w (AR-BaUEN)CENRE-983  |z 9783642366932  |t 16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013 
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