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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)
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)
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 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)
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)