License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2015.102
URN: urn:nbn:de:0030-drops-55750
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5575/
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Giannopoulou, Archontia C. ; Mertzios, George B. ; Niedermeier, Rolf

Polynomial Fixed-parameter Algorithms: A Case Study for Longest Path on Interval Graphs

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Abstract

We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time.
The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus on a fundamental graph problem: Longest Path; it is NP-hard in general but known to be solvable in O(n^4) time on n-vertex interval graphs. We show how to solve Longest Path on Interval Graphs, parameterized by vertex deletion number k to proper interval graphs, in O(k^9n) time. Notably, Longest Path is trivially solvable in linear time on proper interval graphs, and the parameter value k can be approximated up to a factor of 4 in linear time. From a more general perspective, we believe that using parameterized complexity analysis for polynomial-time solvable problems offers a very fertile ground for future studies for all sorts of algorithmic problems. It may enable a refined understanding of efficiency aspects for polynomial-time solvable problems, similarly to what classical parameterized complexity analysis does for NP-hard problems.

BibTeX - Entry

@InProceedings{giannopoulou_et_al:LIPIcs:2015:5575,
  author =	{Archontia C. Giannopoulou and George B. Mertzios and Rolf Niedermeier},
  title =	{{Polynomial Fixed-parameter Algorithms: A Case Study for Longest Path on Interval Graphs}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{102--113},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Thore Husfeldt and Iyad Kanj},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5575},
  URN =		{urn:nbn:de:0030-drops-55750},
  doi =		{10.4230/LIPIcs.IPEC.2015.102},
  annote =	{Keywords: fixed-parameter algorithm, preprocessing, data reduction, polynomial-time algorithm, longest path problem, interval graphs, proper interval vertex del}
}

Keywords: fixed-parameter algorithm, preprocessing, data reduction, polynomial-time algorithm, longest path problem, interval graphs, proper interval vertex del
Collection: 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Issue Date: 2015
Date of publication: 19.11.2015

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