Kernelizations for the hybridization number problem on multiple nonbinary trees

Leo Van Iersel*, Steven Kelk, Celine Scornavacca

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Given a finite set X, a collection T of rooted phylogenetic trees on X and an integer k, the HYBRIDIZATION NUMBER problem asks if there exists a phylogenetic network on X that displays all trees from T and has reticulation number at most k. We show two kernelization algorithms for HYBRIDIZATION NUMBER, with kernel sizes 4k(5k)(t) and 20k(2)(Delta(+) - 1) respectively, with t the number of input trees and Delta(+) their maximum outdegree. Experiments on simulated data demonstrate the practical relevance of our kernelization algorithms. In addition, we present an n(f(k))t-time algorithm, with n = vertical bar X vertical bar and f some computable function of k. 

Original languageEnglish
Pages (from-to)1075-1089
Number of pages15
JournalJournal of Computer and System Sciences
Volume82
Issue number6
DOIs
Publication statusPublished - 1 Sep 2016

Keywords

  • ALGORITHMS
  • EVENTS
  • EVOLUTION
  • Fixed-parameter tractability
  • Hybridization number
  • Kernelization
  • MINIMUM NUMBER
  • PHYLOGENETIC NETWORKS
  • Phylogenetic network
  • Phylogenetic tree

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