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.2021.80
URN: urn:nbn:de:0030-drops-146614
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14661/
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Wang, Yishu ; Mary, Arnaud ; Sagot, Marie-France ; Sinaimeri, Blerina

A General Framework for Enumerating Equivalence Classes of Solutions

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LIPIcs-ESA-2021-80.pdf (0.7 MB)

Abstract

When a problem has more than one solution, it is often important, depending on the underlying context, to enumerate (i.e., to list) them all. Even when the enumeration can be done in polynomial delay, that is, spending no more than polynomial time to go from one solution to the next, this can be costly as the number of solutions themselves may be huge, including sometimes exponential. Furthermore, depending on the application, many of these solutions can be considered equivalent. The problem of an efficient enumeration of the equivalence classes or of one representative per class (without generating all the solutions), although identified as a need in many areas, has been addressed only for very few specific cases. In this paper, we provide a general framework that solves this problem in polynomial delay for a wide variety of contexts, including optimization ones that can be addressed by dynamic programming algorithms, and for certain types of equivalence relations between solutions.

BibTeX - Entry

@InProceedings{wang_et_al:LIPIcs.ESA.2021.80,
  author =	{Wang, Yishu and Mary, Arnaud and Sagot, Marie-France and Sinaimeri, Blerina},
  title =	{{A General Framework for Enumerating Equivalence Classes of Solutions}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{80:1--80:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14661},
  URN =		{urn:nbn:de:0030-drops-146614},
  doi =		{10.4230/LIPIcs.ESA.2021.80},
  annote =	{Keywords: Enumeration algorithms, Equivalence relation, Dynamic programming}
}

Keywords: Enumeration algorithms, Equivalence relation, Dynamic programming
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021

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