A fixed-parameter tractability result for multicommodity demand flow in trees

Authors:
Jiong Guo;Rolf Niedermeier
Affiliations:
Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany
Venue:
Information Processing Letters
Year:
2006

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Abstract

We study an NP-hard (and MaxSNP-hard) problem in trees--MULTICOMMODITY DEMAND FLOW---dealing with demand flows between pairs of nodes and trying to maximize the value of the routed flows. This problem has been intensively studied for trees as well as for general graphs mainly from the viewpoint of polynomial-time approximation algorithms. By way of contrast, we provide an exact dynamic programming algorithm for this problem that works well whenever some natural problem parameter is small, a reasonable assumption in several applications. More specifically, we prove fixed-parameter tractability with respect to the maximum number of the input flows at any tree node.