Technical Report CS0688

TR#:CS0688
Class:CS
Title: 2-TREES OPTIMAL T-JOIN AND INTEGRAL PACKING OF T-CUTS
Authors: E. Korach
PDF - RevisedCS0688.revised.pdf
Abstract: Let $G$ be an undirected graph, $T$ and even subset of vertices and $F$ an optimal $T$-join, which is a forest of 2 trees. The main theorem of this paper characterizes the cases, where $(G,T)$ has an optimal packing of $T$-cuts which is integral. This theorem unifies and generalizes a theorem of P. Seymour on packing of T-cuts and a theorem of A. Frank on planar edge disjoint paths. It also solves positively a conjecture by A. Frank. The proof of the main theorem implies a polynomial algorithm for optimal integral packing of T-cuts for the case where the optimal $T$-join consists of 2 trees. This algorithm is in fact a simple post optimality method, that can be applied to existing algorithms for 1/2 integral packing of T-cuts and also solves polynomially a certain planar integral multicommodity flow problem.
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