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Given a set of species and their similarity data, an important problem in evolutionary biology is how to reconstruct a phylogeny (also called evolutionary tree) so that species are close in the phylogeny if and only if they have high similarity. Assume that the similarity data are represented as a graph G = (V, E) where each vertex represents a species and(More)
The problem of computing a matching of maximum weight in a given edge-weighted graph is not known to be P-hard or in RNC. This paper presents four parallel approximation algorithms for this problem. The rst is an RNC-approximation scheme, i.e., an RNC algorithm that computes a matching of weight at least 1 0 times the maximum for any given constant > 0. The(More)
We present an O(n 3)-time approximation algorithm for the maximum traveling salesman problem whose approximation ratio is asymptotically 61 81 , where n is the number of vertices in the input complete edge-weighted (undirected) graph. We also present an O(n 3)-time approximation algorithm for the metric case of the problem whose approximation ratio is(More)
A reticulate network N of multiple phylogenetic trees may have nodes with two or more parents (called reticulation nodes). There are two ways to define the reticulation number of N. One way is to define it as the number of reticulation nodes in N in this case, a reticulate network with the smallest reticulation number is called an optimal type-I reticulate(More)
This paper deals with the maximum triangle packing problem. For this problem, Hassin and Rubinstein gave a randomized polynomial-time approximation algorithm that achieves an expected ratio of 43 83 (1−) (≈ 0.518(1−)) for any constant > 0. By modifying their algorithm, we obtain a new randomized polynomial-time approximation algorithm for the problem which(More)
We study a constrained bipartite matching problem where the input is a weighted bipartite graph G = (U, V, E), U is a set of vertices following a sequential order, V is another set of vertices partitioned into a collection of disjoint subsets, each following a sequential order, and E is a set of edges between U and V with non-negative weights. The objective(More)