Bulletin of Mathematical Biology

, Volume 78, Issue 5, pp 961–969 | Cite as

On Determining if Tree-based Networks Contain Fixed Trees

  • Maria Anaya
  • Olga Anipchenko-Ulaj
  • Aisha Ashfaq
  • Joyce Chiu
  • Mahedi Kaiser
  • Max Shoji Ohsawa
  • Megan Owen
  • Ella Pavlechko
  • Katherine St. John
  • Shivam Suleria
  • Keith Thompson
  • Corrine Yap
Original Article

Abstract

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is N based on T? We show that it is \(\textit{NP}\)-hard to decide, by reduction from 3-Dimensional Matching (3DM) and further that the problem is fixed-parameter tractable.

Keywords

Phylogenetic tree Phylogenetic network Analysis of algorithms 3-Dimensional Matching 

References

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Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  • Maria Anaya
    • 1
  • Olga Anipchenko-Ulaj
    • 2
  • Aisha Ashfaq
    • 1
  • Joyce Chiu
    • 3
  • Mahedi Kaiser
    • 4
  • Max Shoji Ohsawa
    • 3
  • Megan Owen
    • 4
  • Ella Pavlechko
    • 5
  • Katherine St. John
    • 4
    • 6
  • Shivam Suleria
    • 3
  • Keith Thompson
    • 7
  • Corrine Yap
    • 5
  1. 1.Queensborough Community CollegeCity University of New York (CUNY)BaysideUSA
  2. 2.City College of New YorkCity University of New York (CUNY)New YorkUSA
  3. 3.Brooklyn CollegeCity University of New York (CUNY)BrooklynUSA
  4. 4.Department of Mathematics and Computer Science, Lehman CollegeCity University of New York (CUNY)BronxUSA
  5. 5.Sarah Lawrence CollegeBronxvilleUSA
  6. 6.Division of Invertebrate ZoologyAmerican Museum of Natural HistoryNew YorkUSA
  7. 7.College of Staten IslandCity University of New York (CUNY)Staten IslandUSA

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