Fixed‐parameter tractability and data reduction for multicut in trees
Jiong Guo, Rolf Niedermeier · Networks · 2005
Abstract We study an NP‐complete (and MaxSNP‐hard) communication problem on tree networks, the so‐called MULTICUT IN TREES: given an undirected tree and some pairs of nodes of the tree, find out whether there is a set of at mostktree edges whose removal separates all given pairs of nodes. MULTICUT 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 a simple fixed‐parameter algorithm for MULTICUT IN TREES showing fixed‐parameter tractability with respect to parameterk. Moreover, based on some polynomial time data reduction rules, which appear to be of particular interest from an applied point of view, we show a problem kernel for MULTICUT IN TREES by an intricate mathematical analysis. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(3), 124–135 2005