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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)

a r t i c l e i n f o a b s t r a c t Given a set of n strings of length L and a radius d, the closest string problem (CSP for short) asks for a string t sol that is within a Hamming distance of d to each of the given strings. It is known that the problem is NP-hard and its optimization version admits a polynomial time approximation scheme (PTAS).… (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)

- Zhi-Zhong Chen, Tao Jiang, Guohui Lin, Jianjun Wen, Dong Xu, Jinbo Xu +1 other
- Theor. Comput. Sci.
- 2003

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)

- Zhi-Zhong Chen, Michael R. Fellows, Bin Fu, Haitao Jiang, Yang Liu, Lusheng Wang +1 other
- AAIM
- 2010