Parsimony score of phylogenetic networks: Hardness results and a linear-time heuristic

Guohua Jin, Luay Nakhleh, Sagi Snir, Tamir Tuller

Research output: Contribution to journalArticlepeer-review


Phylogenies-the evolutionary histories of groups of organisms-play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set of species can be represented by a binary tree. Although many biological processes can be effectively modeled and summarized in this fashion, others cannot: recombination, hybrid speciation, and horizontal gene transfer result in networks of relationships rather than trees of relationships. In previous works, we formulated a maximum parsimony (MP) criterion for reconstructing and evaluating phylogenetic networks, and demonstrated its quality on biological as well as synthetic data sets. In this paper, we provide further theoretical results as well as a very fast heuristic algorithm for the MP criterion of phylogenetic networks. In particular, we provide a novel combinatorial definition of phylogenetic networks in terms of "forbidden cycles," and provide detailed hardness and hardness of approximation proofs for the "small" MP problem. We demonstrate the performance of our heuristic in terms of time and accuracy on both biological and synthetic data sets. Finally, we explain the difference between our model and a similar one formulated by Nguyen et al., and describe the implications of this difference on the hardness and approximation results.

Original languageEnglish
Article number4668337
Pages (from-to)495-505
Number of pages11
JournalIEEE/ACM Transactions on Computational Biology and Bioinformatics
Issue number3
StatePublished - Jul 2009

Bibliographical note

Funding Information:
The authors would like to thank Raphy Yuster for some helpful discussion. This work was supported in part by the Rice Terascale Cluster funded by the US National Science Foundation (NSF) under grant EIA-0216467, Intel, and HP. Luay Nakhleh was supported in part by the US Department of Energy under grant DE-FG02-06ER25734, NSF under grant CCF-0622037, the George R. Brown School of Engineering Roy E. Campbell Faculty Development Award, and the Department of Computer Science at Rice University. Tamir Tuller was supported by the Edmond J. Safra Bioinformatics program at Tel Aviv University.


  • Hardness and approximation
  • Horizontal gene transfer
  • Maximum parsimony
  • Phylogenetic networks

ASJC Scopus subject areas

  • Biotechnology
  • Genetics
  • Applied Mathematics


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