Stochastic Modeling of Branch-and-Bound Algorithms with Best-First Search
IEEE Transactions on Software Engineering - Special issue on COMPSAC 1982 and 1983
The complexity of ultrametric partitions on graphs
Information Processing Letters
Efficient Branch-and-Bound Algorithms on a Two-Level Memory System
IEEE Transactions on Software Engineering
Parallel depth first search. Part I. implementation
International Journal of Parallel Programming
A randomized parallel branch-and-bound procedure
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Analysis and Implementation of Branch-and-Bound Algorithms on a Hypercube Multicomputer
IEEE Transactions on Computers
SIAM Journal on Discrete Mathematics
Fast parallel recognition of ultrametrics and tree metrics
SIAM Journal on Discrete Mathematics
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Evaluation of a Parallel Branch-and-Bound Algorithm on a Class of Multiprocessors
IEEE Transactions on Parallel and Distributed Systems
MANIP A Multicomputer Architecture for Solving Combinatonal Extremum-Search Problems
IEEE Transactions on Computers
Distributed Enumeration on Between Computers
IEEE Transactions on Computers
An efficient exact algorithm for the minimum ultrametric tree problem
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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The construction of evolutionary trees is important for computational biology, especially for the development of biological taxonomies. The ultrametric tree (UT) is a commonly used model for evolutionary trees assuming that the rate of evolution is constant (molecular clock hypothesis). However, the construction of minimum ultrametric trees (MUTs, principle of minimum evolution) has been shown to be NP-hard even from a metric distance matrix. The branch-and-bound algorithm is generally used to solve a wide variety of NP-hard problems. In previous work, a sequential branch-and-bound algorithm for constructing MUTs (BBU) was presented and the experimental results showed that it is useful for MUT construction. Hence, in this study, an efficient parallel branch-and-bound algorithm (PBBU) for constructing MUTs or near-MUTs from a metric distance matrix was designed. A random data set as well as some practical data sets of Human + Chimpanzee Mitochondrial and Bacteriophage T7 DNAs were used to test the PBBU. The experimental results show that the PBBU found an optimal solution for 36 species on 16 PCs within a reasonable time. To the best of our knowledge, no algorithm has been found to solve this problem even for 25 species. Moreover, the PBBU achieved satisfying speed-up ratios for most of the test cases.