Parameterized complexity: exponential speed-up for planar graph problems

Authors:
Jochen Alber;Henning Fernau;Rolf Niedermeier
Affiliations:
Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany
Venue:
Journal of Algorithms
Year:
2004

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Abstract

We discuss general techniques, centered around the "Layerwise Separation Property" (LSP) of a planar graph problem, that allow to develop algorithms with running time c√k|G|, given an instance G of a problem on planar graphs with parameter k. Problems having LSP include PLANAR VERTEX COVER. PLANAR INDEPENDENT SET, and PLANAR DOMINATING SET. Extensions of our speed-up technique to basically all fixed-parameter tractable planar graph problems are also exhibited. Moreover, we relate, e.g., the domination number or the vertex cover number, with the treewidth of a plane graph.