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Linear problem kernels for NP-hard problems on planar graphs. (English) Zbl 1171.68488
Arge, Lars (ed.) et al., Automata, languages and programming. 34th international colloquium, ICALP 2007, Wrocław, Poland, July 9–13, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73419-2/pbk). Lecture Notes in Computer Science 4596, 375-386 (2007).
Summary: We develop a generic framework for deriving linear-size problem kernels for NP-hard problems on planar graphs. We demonstrate the usefulness of our framework in several concrete case studies, giving new kernelization results for Connected Vertex Cover, Minimum Edge Dominating Set, Maximum Triangle Packing, and Efficient Dominating Set on planar graphs. On the route to these results, we present effective, problem-specific data reduction rules that are useful in any approach attacking the computational intractability of these problems.
For the entire collection see [Zbl 1119.68002].

MSC:
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
68Q25 Analysis of algorithms and problem complexity
68R10 Graph theory (including graph drawing) in computer science
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