|Title:||TIGHT INTEGRAL DUALITY GAP IN THE CHINESE POSTMAN PROBLEM
|Authors:||E. Korach and M. Penn
|Abstract:||Let G = (V, E) be a graph and a weight function w : E -+ Z+. Let T C V be an even subset of the vertices of G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. A T-join is a minimal subset of edges that meets every T-cut (a generalization of solutionS to the Chinese postman problem). The main theorem of this paper gives a tight upper bound on the difference between the minimum weight T-join and the maximum weighted integral packing of T-cut. This difference is called the (T-join)integral duality gap. Let nF be the number of components in the optimal T-join, Ttl) =minimum weight T-join and IItI) = max weight integral packing of T-cuts then we have T., -II., < nF -1. This result unifies and generalizes Fulkerson's result for ITI =2 and Seymour's result for ITI = 4. For a certain integral multicommodity flow problem in the plane, which was recently proved to be NP-complete, the above result gives a solution such that for every commodity the flow is less than the demand by at most one unit.|
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