Matrices with the Edmonds-Johnson property
Combinatorica
Recognizing claw-free perfect graphs
Journal of Combinatorial Theory Series A
A description of claw-free perfect graphs
Journal of Combinatorial Theory Series B
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Graphs and Hypergraphs
An improved tight closure algorithm for integer octagonal constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Incremental Satisfiability and Implication for UTVPI Constraints
INFORMS Journal on Computing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An efficient decision procedure for UTVPI constraints
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
Minimum weighted clique cover on strip-composed perfect graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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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.