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DOI: 10.4230/LIPIcs.ESA.2021.80

A General Framework for Enumerating Equivalence Classes of Solutions

Authors: Yishu Wang, Arnaud Mary, Marie-France Sagot, and Blerina Sinaimeri

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

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.

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Yishu Wang, Arnaud Mary, Marie-France Sagot, and Blerina Sinaimeri. A General Framework for Enumerating Equivalence Classes of Solutions. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 80:1-80:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@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/entities/document/10.4230/LIPIcs.ESA.2021.80},
  URN =		{urn:nbn:de:0030-drops-146614},
  doi =		{10.4230/LIPIcs.ESA.2021.80},
  annote =	{Keywords: Enumeration algorithms, Equivalence relation, Dynamic programming}
}

Document

DOI: 10.4230/LIPIcs.WABI.2021.3

Making Sense of a Cophylogeny Output: Efficient Listing of Representative Reconciliations

Authors: Yishu Wang, Arnaud Mary, Marie-France Sagot, and Blerina Sinaimeri

Published in: LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)

Abstract

Cophylogeny reconciliation is a powerful method for analyzing host-parasite (or host-symbiont) co-evolution. It models co-evolution as an optimization problem where the set of all optimal solutions may represent different biological scenarios which thus need to be analyzed separately. Despite the significant research done in the area, few approaches have addressed the problem of helping the biologist deal with the often huge space of optimal solutions. In this paper, we propose a new approach to tackle this problem. We introduce three different criteria under which two solutions may be considered biologically equivalent, and then we propose polynomial-delay algorithms that enumerate only one representative per equivalence class (without listing all the solutions). Our results are of both theoretical and practical importance. Indeed, as shown by the experiments, we are able to significantly reduce the space of optimal solutions while still maintaining important biological information about the whole space.

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Yishu Wang, Arnaud Mary, Marie-France Sagot, and Blerina Sinaimeri. Making Sense of a Cophylogeny Output: Efficient Listing of Representative Reconciliations. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{wang_et_al:LIPIcs.WABI.2021.3,
  author =	{Wang, Yishu and Mary, Arnaud and Sagot, Marie-France and Sinaimeri, Blerina},
  title =	{{Making Sense of a Cophylogeny Output: Efficient Listing of Representative Reconciliations}},
  booktitle =	{21st International Workshop on Algorithms in Bioinformatics (WABI 2021)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-200-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{201},
  editor =	{Carbone, Alessandra and El-Kebir, Mohammed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021.3},
  URN =		{urn:nbn:de:0030-drops-143564},
  doi =		{10.4230/LIPIcs.WABI.2021.3},
  annote =	{Keywords: Cophylogeny, Enumeration, Equivalence relation, Dynamic programming}
}

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Documents authored by Wang, Yishu

A General Framework for Enumerating Equivalence Classes of Solutions

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Making Sense of a Cophylogeny Output: Efficient Listing of Representative Reconciliations

Abstract

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