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.CPM.2019.28
URN: urn:nbn:de:0030-drops-104998
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10499/
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Bernardini, Giulia ; Bonizzoni, Paola ; Della Vedova, Gianluca ; Patterson, Murray

A Rearrangement Distance for Fully-Labelled Trees

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LIPIcs-CPM-2019-28.pdf (0.5 MB)

Abstract

The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the widely studied setting of classical phylogenetics, where trees are leaf-labelled, tumoral trees are fully labelled, i.e., every vertex has a label.
In this paper we provide a rearrangement distance measure between two fully-labelled trees. This notion originates from two operations: one which modifies the topology of the tree, the other which permutes the labels of the vertices, hence leaving the topology unaffected. While we show that the distance between two trees in terms of each such operation alone can be decided in polynomial time, the more general notion of distance when both operations are allowed is NP-hard to decide. Despite this result, we show that it is fixed-parameter tractable, and we give a 4-approximation algorithm when one of the trees is binary.

BibTeX - Entry

@InProceedings{bernardini_et_al:LIPIcs:2019:10499,
  author =	{Giulia Bernardini and Paola Bonizzoni and Gianluca Della Vedova and Murray Patterson},
  title =	{{A Rearrangement Distance for Fully-Labelled Trees}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Nadia Pisanti and Solon P. Pissis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10499},
  URN =		{urn:nbn:de:0030-drops-104998},
  doi =		{10.4230/LIPIcs.CPM.2019.28},
  annote =	{Keywords: Tree rearrangement distance, Cancer progression, Approximation algorithms, Computational complexity}
}

Keywords: Tree rearrangement distance, Cancer progression, Approximation algorithms, Computational complexity
Collection: 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)
Issue Date: 2019
Date of publication: 06.06.2019

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