Titlebook: Integer Programming and Combinatorial Optimization; 8th International IP Karen Aardal,Bert Gerards Conference proceedings 2001 Springer-Ver

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Approximate ,-MSTs and ,-Steiner Trees via the Primal-Dual Method and Lagrangean Relaxation,thms for this problem. We show that Garg’s al- gorithms can be explained simply with ideas introduced by Jain and Vazirani for the metric uncapacitated facility location and .-median problems [.], in particular via a Lagrangean relaxation technique to- gether with the primal-dual method for approxim

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Combined Connectivity Augmentation and Orientation Problems, meet a specified target connectivity, and connectivity orientation, where the goal is to find an orientation of an undirected or mixed graph that satisfies some specified edge-connection property. In the present work an attempt is made to link the above two branches, by considering degree-specified

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Bisubmodular Function Minimization,odular function minimization due to Iwata, Fleischer, and Fujishige. A bisubmodular function arises as a rank function of a delta-matroid. The scaling algorithm naturally leads to the first combinatorial polynomial-time algorithm for testing membership in delta- matroid polyhedra. Unlike the case of

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Integral Polyhedra Related to Even Cycle and Even Cut Matroids,.-path; or the union of an even .-path and an odd circuit which share at most one vertex. Let . be a subset of vertices of even cardinality. An . is a cut of the form δ(.) where |. ∩ .| is odd and . contains exactly one of . or .. We give excluded minor characterizations for when the families of odd