Graph separators: a parameterized view

Authors:
Jochen Alber;Henning Fernau;Rolf Niedermeier
Affiliations:
Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany;University of Newcastle, School of Electrical Engineering and Computer Science, University Drive, Callaghan, NSW 2308, Australia;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany
Venue:
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Year:
2003

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Abstract

Graph separation is a well-known tool to make (hard) graph problems accessible to a divide-and-conquer approach. We show how to use graph separator theorems in combination with (linear) problem kernels in order to develop fixed parameter algorithms for many well-known NP-hard (planar) graph problems. We coin the key notion of glueable select&verify graph problems and derive from that a prospective way to easily check whether a planar graph problem will allow for a fixed parameter algorithm of running time c√kno(1) for constant c. One of the main contributions of the paper is to exactly compute the base c of the exponential term and its dependence on the various parameters specified by the employed separator theorem and the underlying graph problem. We discuss several strategies to improve on the involved constant c.