Combinatorial Algorithms for the Unsplittable Flow Problem

We provide combinatorial algorithms for the unsplittable flow problem (UFP) that either match or improve the previously best results. In the UFP we are given a (possibly directed) capacitated graph with n vertices and m edges, and a set of terminal pairs each with its own demand and profit. The objective is to connect a subset of the terminal pairs each by a single flow path subject to the capacity constraints such that the total profit of the connected pairs is maximized. We consider three variants of the problem. First is the classical UFP in which the maximum demand is at most than the minimum edge capacity. It was previously known to have an O( m) approximation algorithm; the algorithm is based on the randomized rounding technique and its analysis makes use of the Chernoff bound and the FKG inequality. We provide a combinatorial algorithm that achieves the same approximation ratio and whose analysis is considerably simpler. Second is the extended UFP in which some demands might b...

• Type: Journal
• Year: 2006
• Where: ALGORITHMICA
• Authors: Yossi Azar, Oded Regev
• Keywords: Algorithm, ALGORITHMICA 2006, Classical Ufp, Combinatorial Algorithm