A colored graph approach to perfect phylogeny with persistent characters

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• 作者：Paola Bonizzoni^a ; ^{bonizzoni@disco.unimib.it} ; Anna Paola Carrieri^a ; ^{annapaola.carrieri@disco.unimib.it} ; Gianluca Della Vedova^a ; ^{gianluca.dellavedova@unimib.it} ; Raffaella Rizzi^a ; ^{rizzi@disco.unimib.it} ; Gabriella Trucco^b ; ^{gabriella.trucco@unimi.it}
• 关键词：Perfect phylogeny ; Persistent phylogeny ; Character-based evolution ; Graph theory
• 刊名：Theoretical Computer Science
• 出版年：2017
• 出版时间：7 January 2017
• 年：2017
• 卷：658
• 期：part_PA
• 页码：60-73
• 全文大小：544 K
• 卷排序：658

文摘

A main open question related to character-based tree reconstruction is designing generalizations of the Perfect Phylogeny approach that couple efficient algorithmic solutions to the capability of explaining the input binary data, by allowing back mutations of some characters. Following this goal, the Persistent Phylogeny model and the related tree reconstruction problem (the PPP problem) have been recently introduced: this model allows only one back mutation for each character. The investigation of the combinatorial properties and the complexity of the model is still open: the most important such question is whether the PPP problem is NP-hard. Here we propose a graph-based approach to the PPP problem by showing that instances can be represented by colored graphs, while the solutions are obtained by operations on such graphs. Indeed, we give a graph-based characterization of the solutions to the PPP problem by showing the relationship between certain sequences of graph operations on the instance graphs and traversals of a persistent phylogeny solving these instances. Based on this result and on some combinatorial properties of the instance graphs we are able to give a polynomial time algorithm for a restricted version of the PPP problem.