eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-06-06
28:1
28:15
10.4230/LIPIcs.CPM.2019.28
article
A Rearrangement Distance for Fully-Labelled Trees
Bernardini, Giulia
1
Bonizzoni, Paola
1
Della Vedova, Gianluca
1
Patterson, Murray
1
DISCo, Università degli Studi Milano - Bicocca, Italy
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol128-cpm2019/LIPIcs.CPM.2019.28/LIPIcs.CPM.2019.28.pdf
Tree rearrangement distance
Cancer progression
Approximation algorithms
Computational complexity