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A max-min theorem for integer multiflows

Conference ·
OSTI ID:36234

We consider a multigraph G = (V, E), with the vertex-set V and edge-set E, and a set T {improper_subset} V of terminals, {vert_bar}T{vert_bar} {>=} 2. Given a graph S = (T, U) with U {intersection} E = {O}, called scheme, define an integer S-flow in G as a collection C of edge-disjoint paths in G whose ends are terminals adjacent in S. We address the problem of maximum integer S-flow under the following assumptions: (1) the non-terminal vertices of G have even degrees, and (2) each terminal belongs to atmost two anticliques of S. Due to the assumption, there arises a deep analogy of this problem with matchings in graphs. In fact, it admits formulating as a polymatroid matching problem. We develop an approach analogous to the Berge method of alternating paths, with the notion of {open_quotes}blossom{close_quotes} closely related to that introduced by Edmonds. We characterize max {vert_bar}C{vert_bar} by a max-min relation analogous to the Berge-Tutte formula of the Matching theory.

OSTI ID:
36234
Report Number(s):
CONF-9408161--
Country of Publication:
United States
Language:
English

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