The complexity of ultrametric partitions on graphs
Information Processing Letters
SIAM Journal on Discrete Mathematics
An optimal algorithm for finding compact sets
Information Processing Letters
Fast parallel recognition of ultrametrics and tree metrics
SIAM Journal on Discrete Mathematics
A note on finding compact sets in graphs represented by an adjacency list
Information Processing Letters
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Constructing an evolutionary tree has many techniques, and usually biologists use distance matrix on this activity. The evolutionary tree can assist in taxonomy for biologists to analyze the phylogeny. In this paper, we specifically employ the compact sets to convert the original matrix into several small matrices for constructing evolutionary tree in parallel. By the properties of compact sets, we do not spend much time and do keep the correct relations among species. Besides, we adopt both Human Mitochondrial DNAs and randomly generated matrix as input data in the experiments. In comparison with conventional technique, the experimental results show that utilizing compact sets can definitely construct the evolutionary tree in a reasonable time.