On Problems without Polynomial Kernels (Extended Abstract)

Authors:
Hans L. Bodlaender;Rodney G. Downey;Michael R. Fellows;Danny Hermelin
Affiliations:
Department of Information and Computing Sciences, Utrecht University, TB Utrecht, Netherlands 80.089;School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, Wellington, New Zealand 600;The University of Newcastle, Callaghan, Australia NSW 2308;The University of Haifa, Haifa, Israel 31905
Venue:
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Year:
2008

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Abstract

Kernelization is a central technique used in parameterized algorithms, and in other approaches for coping with NP-hard problems. In this paper, we introduce a new method which allows us to show that many problems do not have polynomial size kernels under reasonable complexity-theoretic assumptions. These problems include k -Path, k -Cycle, k -Exact Cycle, k -Short Cheap Tour, k -Graph Minor Order Test, k -Cutwidth, k -Search Number, k -Pathwidth, k -Treewidth, k -Branchwidth, and several optimization problems parameterized by treewidth or cliquewidth.