2026-08-17T07:42:16Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:5566 2024-03-06T10:36:34Z ddc:004 open_access

Bidimensionality and Parameterized Algorithms (Invited Talk) Thilikos, Dimitrios M. Parameterized algorithms Subexponential FPT-algorithms Kernelization Linear kenrels Bidimensionality Graph Minors We provide an exposition of the main results of the theory of bidimensionality in parameterized algorithm design. This theory applies to graph problems that are bidimensional in the sense that i) their solution value is not increasing when we take minors or contractions of the input graph and ii) their solution value for the (triangulated) (k x k)-grid graph grows as a quadratic function of k. Under certain additional conditions, mainly of logical and combinatorial nature, such problems admit subexponential parameterized algorithms and linear kernels when their inputs are restricted to certain topologically defined graph classes. We provide all formal definitions and concepts in order to present these results in a rigorous way and in their latest update. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Dimitrios M. Thilikos 2015 Is Part Of LIPIcs, Volume 43, 10th International Symposium on Parameterized and Exact Computation (IPEC 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.IPEC.2015.1 urn:nbn:de:0030-drops-55663 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2015.1 eng https://creativecommons.org/licenses/by/3.0/legalcode