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Documents authored by Bonizzoni, Paola


Document
On Two Measures of Distance Between Fully-Labelled Trees

Authors: Giulia Bernardini, Paola Bonizzoni, and Paweł Gawrychowski

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)


Abstract
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for comparing rooted trees representing the evolution of mutations in tumor phylogenies. Bernardini et al. [CPM 2019] recently introduced a notion of the rearrangement distance for fully-labelled trees motivated by this necessity. This notion originates from two operations: one that permutes the labels of the nodes, the other that affects the topology of the tree. Each operation alone defines a distance that can be computed in polynomial time, while the actual rearrangement distance, that combines the two, was proven to be NP-hard. We answer two open question left unanswered by the previous work. First, what is the complexity of computing the permutation distance? Second, is there a constant-factor approximation algorithm for estimating the rearrangement distance between two arbitrary trees? We answer the first one by showing, via a two-way reduction, that calculating the permutation distance between two trees on n nodes is equivalent, up to polylogarithmic factors, to finding the largest cardinality matching in a sparse bipartite graph. In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2020], we obtain an 𝒪̃(n^{4/3+o(1}) time algorithm for computing the permutation distance between two trees on n nodes. Then we answer the second question positively, and design a linear-time constant-factor approximation algorithm that does not need any assumption on the trees.

Cite as

Giulia Bernardini, Paola Bonizzoni, and Paweł Gawrychowski. On Two Measures of Distance Between Fully-Labelled Trees. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bernardini_et_al:LIPIcs.CPM.2020.6,
  author =	{Bernardini, Giulia and Bonizzoni, Paola and Gawrychowski, Pawe{\l}},
  title =	{{On Two Measures of Distance Between Fully-Labelled Trees}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.6},
  URN =		{urn:nbn:de:0030-drops-121318},
  doi =		{10.4230/LIPIcs.CPM.2020.6},
  annote =	{Keywords: Tree distance, Cancer progression, Approximation algorithms, Fine-grained complexity}
}
Document
A Rearrangement Distance for Fully-Labelled Trees

Authors: Giulia Bernardini, Paola Bonizzoni, Gianluca Della Vedova, and Murray Patterson

Published in: LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)


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.

Cite as

Giulia Bernardini, Paola Bonizzoni, Gianluca Della Vedova, and Murray Patterson. A Rearrangement Distance for Fully-Labelled Trees. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{bernardini_et_al:LIPIcs.CPM.2019.28,
  author =	{Bernardini, Giulia and Bonizzoni, Paola and Della Vedova, Gianluca and Patterson, Murray},
  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 =	{Pisanti, Nadia and P. Pissis, Solon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.28},
  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}
}
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