Maximum flows on disjoint paths

Authors:
Guyslain Naves;Nicolas Sonnerat;Adrian Vetta
Affiliations:
Department of Mathematics and Statistics, McGill University;Department of Mathematics and Statistics, McGill University;Department of Mathematics and Statistics, and School of Computer Science, McGill University
Venue:
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Year:
2010

Citing 7
Cited 0

Network flows: theory, algorithms, and applications

Network flows: theory, algorithms, and applications
Single-source unsplittable flow

FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems

Journal of Computer and System Sciences
Complexity and approximability of k-splittable flows

Theoretical Computer Science
Hardness of routing with congestion in directed graphs

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Edge-Disjoint Paths in Planar Graphs with Constant Congestion

SIAM Journal on Computing
Single-source k-splittable min-cost flows

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the question: What is the maximum flow achievable in a network if the flow must be decomposable into a collection of edge-disjoint paths? Equivalently, we wish to find a maximum weighted packing of disjoint paths, where the weight of a path is the minimum capacity of an edge on the path. Our main result is an Ω(log n) lower bound on the approximability of the problem. We also show this bound is tight to within a constant factor. Surprisingly, the lower bound applies even for the simple case of undirected, planar graphs. Our results extend to the case in which the flow must decompose into at most k disjoint paths. There we obtain Θ(log k) upper and lower approximability bounds.