On the Descriptive Complexity of Color Coding

Max Bannach, Till Tantau

Abstract

Color coding is an algorithmic technique used in parameterized complexity theory to detect “small” structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable, small color pattern. We transfer color coding to the world of descriptive complexity theory by characterizing – purely in terms of the syntactic structure of describing formulas – when the powerful second-order quantifiers representing a random coloring can be replaced by equivalent, simple first-order formulas. Building on this result, we identify syntactic properties of first-order quantifiers that can be eliminated from formulas describing parameterized problems. The result applies to many packing and embedding problems, but also to the long path problem. Together with a new result on the parameterized complexity of formula families involving only a fixed number of variables, we get that many problems lie in fpt just because of the way they are commonly described using logical formulas.

Original languageEnglish
Title of host publication36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)
EditorsRolf Niedermeier, Christophe Paul
Number of pages16
Volume126
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Publication date01.03.2019
Pages11:1--11:16
Article number11
ISBN (Print)978-3-95977-100-9
DOIs
Publication statusPublished - 01.03.2019
Event36th International Symposium on Theoretical Aspects of Computer Science - Berlin, Germany
Duration: 13.03.201916.03.2019
Conference number: 153790

DFG Research Classification Scheme

  • 409-01 Theoretical Computer Science

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