منابع مشابه
Submodular Unsplittable Flow on Trees
We study the Unsplittable Flow problem (UFP) on trees with a submodular objective function. The input to this problem is a tree with edge capacities and a collection of tasks, each characterized by a source node, a sink node, and a demand. A subset of the tasks is feasible if the tasks can simultaneously send their demands from the source to the sink without violating the edge capacities. The g...
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We study some linear programming relaxations for the Unsplittable Flow problem on trees (UFPtree). Inspired by results obtained by Chekuri, Ene, and Korula for Unsplittable Flow on paths (UFP-path), we present a relaxation with polynomially many constraints that has an integrality gap bound of O(logn ·min{logm, logn}) where n denotes the number of tasks and m denotes the number of edges in the ...
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We consider the approximability of the Unsplittable Flow Problem (UFP) on tree graphs, and give a deterministic quasi-polynomial time approximation scheme for the problem when the number of leaves in the tree graph is at most poly-logarithmic in n (the number of demands), and when all edge capacities and resource requirements are suitably bounded. Our algorithm generalizes a recent technique th...
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The max-ow min-cut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity. Menger's theorem provides a good characterization for the following single{source disjoint paths problem: given a graph G, with a source vertex s and terminals t 1 ; : : :; t k , decide whether there exist edge{disjoint s-t i paths, for i = 1; : : :; k. W...
متن کاملOn the Single-Source Unsplittable Flow Problem
If the necessary cut condition is satisfied, we show how to compute an unsplittable flow satisfying the demands such that the total flow through any edge exceeds its capacity by at most the maximum demand. For graphs in which all capacities are at least the maximum demand, we therefore obtain an unsplittable flow with congestion at most 2, and this result is best possible. Furthermore, we show ...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2018
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-017-1218-4