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Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors Katrin Casel, Joel D. Day , Pamela Fleischmann , Tomasz Kociumaka , Florin Manea , Markus L. Schmid

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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Mathematics of computing → Combinatorics on words
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Graph and String Parameters
  • NP-Completeness
  • Approximation Algorithms

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Abstract

We investigate the locality number, a recently introduced structural parameter for strings (with applications in pattern matching with variables), and its connection to two important graph-parameters, cutwidth and pathwidth. These connections allow us to show that computing the locality number is NP-hard but fixed-parameter tractable (when the locality number or the alphabet size is treated as a parameter), and can be approximated with ratio O(sqrt{log{opt}} log n). As a by-product, we also relate cutwidth via the locality number to pathwidth, which is of independent interest, since it improves the best currently known approximation algorithm for cutwidth. In addition to these main results, we also consider the possibility of greedy-based approximation algorithms for the locality number.

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Katrin Casel, Joel D. Day, Pamela Fleischmann, Tomasz Kociumaka, Florin Manea, and Markus L. Schmid. Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 109:1-109:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICALP.2019.109

Author Details

Katrin Casel
  • Hasso Plattner Institute, University of Potsdam, Germany
Joel D. Day
  • Department of Computer Science, Loughborough University, UK
Pamela Fleischmann
  • Department of Computer Science, Kiel University, Germany
Tomasz Kociumaka
  • Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel
  • Institute of Informatics, University of Warsaw, Poland
Florin Manea
  • Department of Computer Science, Kiel University, Germany
Markus L. Schmid
  • Trier University, Germany

Funding

  • Kociumaka, Tomasz: Supported by ISF grants no. 824/17 and 1278/16 and by an ERC grant MPM under the EU’s Horizon 2020 Research and Innovation Programme (grant no. 683064).
  • Manea, Florin: Supported by the DFG grant MA 5725/2-1.

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