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Lower bounds for dynamic programming on planar graphs of bounded cutwidth

Lower bounds for dynamic programming on planar graphs of bounded cutwidth

Authors :
van Geffen, B.A.M.
Jansen, Bart M.P.
de Kroon, A.A.W.M.
Morel, Rolf
Paul, Christophe
Pilipczuk, Michal
Algorithms, Geometry and Applications
Algorithms
Source :
arXiv, 2018:1806.10513v1. Cornell University Library, Journal of Graph Algorithms and Applications, 24(3), 461-482. Brown University, 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)
Publication Year :
2018

Abstract

Many combinatorial problems can be solved in time O∗(ctw) on graphs of treewidth tw, for a problem-specific constant c. In several cases, matching upper and lower bounds on c are known based on the Strong Exponential Time Hypothesis (SETH). In this paper we investigate the complexity of solving problems on graphs of bounded cutwidth, a graph parameter that takes larger values than treewidth. We strengthen earlier treewidth-based lower bounds to show that, assuming SETH, Independent Set cannot be solved in O∗((2 − ε)ctw) time, and Dominating Set cannot be solved in O∗((3 − ε)ctw) time. By designing a new crossover gadget, we extend these lower bounds even to planar graphs of bounded cutwidth or treewidth. Hence planarity does not help when solving Independent Set or Dominating Set on graphs of bounded width. This sharply contrasts the fact that in many settings, planarity allows problems to be solved much more efficiently.

Details

Language :
English
ISSN :
15261719
Database :
OpenAIRE
Journal :
arXiv, 2018:1806.10513v1. Cornell University Library, Journal of Graph Algorithms and Applications, 24(3), 461-482. Brown University, 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)
Accession number :
edsair.doi.dedup.....15c5c81cf9815e0ee1c19506a4c2daeb