A Property Tester for Tree-Likeness of Quartet Topologies

作者：Chang Maw Shang; Lin Chuang Chieh^*; Rossmanith Peter

来源：Theory of Computing Systems, 2011, 49(3): 576-587.

DOI：10.1007/s00224-010-9276-5

• Randomized algorithm
• Property testing
• Evolutionary tree
• Quartet method

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 P and a parameter 0 < epsilon < 1, by examining function values of f over o(vertical bar D vertical bar) elements in D, determine whether f satisfies P or differs from any one which satisfies P in at least epsilon vertical bar D vertical bar 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 fQ 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)(4)) for some constant c > 0, and present the first property tester for tree-likeness of quartet topologies. Our property tester makes at most O(n(3)/epsilon) queries, and is of one-sided error and non-adaptive.

• 出版日期2011-10