A Property Tester for Tree-Likeness of Quartet Topologies

  • Authors:

  • Maw-Shang Chang;Chuang-Chieh Lin;Peter Rossmanith

  • Affiliations:

  • National Chung Cheng University, Department of Computer Science and Information Engineering, 621, Ming-Hsiung, Chiayi, Taiwan;National Chung Cheng University, Department of Computer Science and Information Engineering, 621, Ming-Hsiung, Chiayi, Taiwan;RWTH Aachen University, Department of Computer Science, Ahornstr. 55, 52056, Aachen, Germany

  • Venue:
  • Theory of Computing Systems
  • Year:
  • 2011

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Abstract

Property testing is a rapid growing field in theoretical computer science. It considers the following task: given a function f over a domain D, a property ℘ and a parameter 0εf over o(|D|) elements in D, determine whether f satisfies ℘ or differs from any one which satisfies ℘ in at least ε|D| elements. An algorithm that fulfills this task is called a property tester. We focus on tree-likeness of quartet topologies, which is a combinatorial property originating from evolutionary tree construction. The input function is f Q , which assigns one of the three possible topologies for every quartet over an n-taxon set S. We say that f Q satisfies tree-likeness if there exists an evolutionary tree T whose induced quartet topologies coincide with f Q . In this paper, we prove the existence of a set of quartet topologies of error number at least $c{n\choose 4}$ for some constant c0, and present the first property tester for tree-likeness of quartet topologies. Our property tester makes at most O(n 3/ε) queries, and is of one-sided error and non-adaptive.