License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2023.54
URN: urn:nbn:de:0030-drops-187073
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18707/
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Griesbach, Svenja M. ; Hommelsheim, Felix ; Klimm, Max ; Schewior, Kevin

Improved Approximation Algorithms for the Expanding Search Problem

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LIPIcs-ESA-2023-54.pdf (0.8 MB)

Abstract

A searcher faces a graph with edge lengths and vertex weights, initially having explored only a given starting vertex. In each step, the searcher adds an edge to the solution that connects an unexplored vertex to an explored vertex. This requires an amount of time equal to the edge length. The goal is to minimize the weighted sum of the exploration times over all vertices. We show that this problem is hard to approximate and provide algorithms with improved approximation guarantees. For the general case, we give a (2e+ε)-approximation for any ε > 0. For the case that all vertices have unit weight, we provide a 2e-approximation. Finally, we provide a PTAS for the case of a Euclidean graph. Previously, for all cases only an 8-approximation was known.

BibTeX - Entry

@InProceedings{griesbach_et_al:LIPIcs.ESA.2023.54,
  author =	{Griesbach, Svenja M. and Hommelsheim, Felix and Klimm, Max and Schewior, Kevin},
  title =	{{Improved Approximation Algorithms for the Expanding Search Problem}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{54:1--54:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18707},
  URN =		{urn:nbn:de:0030-drops-187073},
  doi =		{10.4230/LIPIcs.ESA.2023.54},
  annote =	{Keywords: Approximation Algorithm, Expanding Search, Search Problem, Graph Exploration, Traveling Repairperson Problem}
}

Keywords: Approximation Algorithm, Expanding Search, Search Problem, Graph Exploration, Traveling Repairperson Problem
Collection: 31st Annual European Symposium on Algorithms (ESA 2023)
Issue Date: 2023
Date of publication: 30.08.2023

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