A 2-Approximation for the Minimum Duplication Speciation Problem

Ouangraoua, Aïda; Swenson, Krister M.; Chauve, Cédric

doi:10.1089/cmb.2011.0108

Cited by 3 publications

(3 citation statements)

References 38 publications

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“…Here, the maximum number of splits not cut by an optimal partition was obtained by exhaustive search for each dataset. We also compared the FP algorithm with another reported in (Ouangraoua et al, 2011). It is based on an algorithm for the unweighted hypergraph min cut problem in (Mak, 2011) and can be used for the same purpose.…”

Section: Step One: Resolve Non-binary Species Tree Nodesmentioning

confidence: 99%

“…Table 1. Performance of the First Partition (FP) algorithm and an algorithm presented in (Ouangraoua et al, 2011). One thousand random datasets were generated for each combination of c and cs, which are the number of leaf species below the non-binary species tree node to be refined and the number of splits found in the input gene tree, respectively.…”

Section: Step One: Resolve Non-binary Species Tree Nodesmentioning

confidence: 99%

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Reconciliation of Gene and Species Trees With Polytomies

Zheng,

Wu,

Zhang

2012

Preprint

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Motivation: Millions of genes in the modern species belong to only thousands of gene families. Genes duplicate and are lost during evolution. A gene family includes instances of the same gene in different species and duplicate genes in the same species. Two genes in different species are ortholog if their common ancestor lies in the most recent common ancestor of the species. Because of complex gene evolutionary history, ortholog identification is a basic but difficult task in comparative genomics. A key method for the task is to use an explicit model of the evolutionary history of the genes being studied, called the gene (family) tree. It compares the gene tree with the evolutionary history of the species in which the genes reside, called the species tree, using the procedure known as tree reconciliation. Reconciling binary gene and specific trees is simple. However, tree reconciliation presents challenging problems when species trees are not binary in practice. Here, arbitrary gene and species tree reconciliation is studied in a binary refinement model. Results:The problem of reconciling gene and species trees is proved NP-hard when species tree is not binary even for the duplication cost. We then present the first efficient method for reconciling a nonbinary gene tree and a non-binary species tree. It attempts to find a binary refinement of the given gene and species trees that minimizes the given reconciliation cost if they are not binary. Our algorithms have been implemented into a software to support quick automated analysis of large data sets.

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Section: Step One: Resolve Non-binary Species Tree Nodesmentioning

confidence: 99%

Section: Step One: Resolve Non-binary Species Tree Nodesmentioning

confidence: 99%

Reconciliation of Gene and Species Trees With Polytomies

Zheng,

Wu,

Zhang

2012

Preprint

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“…Label s-t Cut has attracted much attention from researchers in computer science (see, e.g., [2,4,6,9,12,13,14,15]) and researchers even in chemical engineering (see [10]). The problem finds many applications in image segmentation [19], network connectivity [29], computational biology [22], and network security [1], etc. Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

Approximating the Weighted Minimum Label $s$-$t$ Cut Problem

Zhang

2020

Preprint

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In the weighted (minimum) Label s-t Cut problem, we are given a (directed or undirected) graph G = (V, E), a label set L = {ℓ 1 , ℓ 2 , . . . , ℓ q } with positive label weights {w ℓ }, a source s ∈ V and a sink t ∈ V . Each edge edge e of G has a label ℓ(e) from L. Different edges may have the same label. The problem asks to find a minimum weight label subset L ′ such that the removal of all edges with labels in L ′ disconnects s and t.The unweighted Label s-t Cut problem (i.e., every label has a unit weight) can be approximated within O(n 2/3 ), where n is the number of vertices of graph G. However, it is unknown for a long time how to approximate the weighted Label s-t Cut problem within o(n). In this paper, we provide an approximation algorithm for the weighted Label s-t Cut problem with ratio O(n 2/3 ). The key point of the algorithm is a mechanism to interpret label weight on an edge as both its length and capacity.

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A Tool for Non-binary Tree Reconciliation

Zheng

Zhang

2013

Lecture Notes in Computer Science

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A 2-Approximation for the Minimum Duplication Speciation Problem

Cited by 3 publications

References 38 publications

Reconciliation of Gene and Species Trees With Polytomies

Reconciliation of Gene and Species Trees With Polytomies

Approximating the Weighted Minimum Label $s$-$t$ Cut Problem

A Tool for Non-binary Tree Reconciliation

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