Multiflows and matchings
Let G be a multigraph, with a set T {improper_subset} V(G) of terminals, and S = (T, U) be a graph (called the scheme), with E(G), {intersection} U = {O}. An integer S-flow in G is a collection of edge-disjoint paths linking pairs of terminals adjacent in S. We deal with the following: Find a maximum S-flow in G. For A {improper_subset} T, put {lambda}(A) := min {l_brace}degX : X {improper_subset} V(G), X{intersection}T = A{r_brace} where deg X is the number of edges between X and {bar X}. Assume the G and S satisfy the following conditions: (1) the degree of any v {element_of} V (G)/T is even (2) any terminal belongs to at most two anticliques of S (3){vert_bar}A{intersection}B{vert_bar}{<=}1 for any distinct anticliques A, B of S. Let A denote the hypergraph consisting of anticliques of S, and singletons {l_brace}t{r_brace}, for the terminals t belonging to exactly one anticlique, and A* be its dual (so that A* is a graph with the vertex-set A and the edge-set T). For A {element_of} A, let P{sub A} denote the polymatroid on A with the rank function r{sub a}(X) : = {1/2} ({sub t{element_of}X}{sup {Sigma}} {lambda}) + {lambda}(A / X) - {lambda}(A), X {improper_subset} A. A nonnegative integer function on T is called a poly-matchoid if its restriction to any A {element_of} A is independent in P{sub A}. The above Problem is polynomially equivalent to the problem of finding a maximum polymatchoid in A*. If, in addition {vert_bar}A{vert_bar} {<=} 4 for every anticlique A of S, then it is reducible to the maximum b-matching problem for a graph with O({vert_bar}T{vert_bar}) edges.
- OSTI ID:
- 36628
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0427
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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