Trees, stars, and multiple biological sequence alignment
SIAM Journal on Applied Mathematics
Algorithms for finding patterns in strings
Handbook of theoretical computer science (vol. A)
Approximation algorithms for multiple sequence alignment
Theoretical Computer Science
Improved approximation algorithms for tree alignment
Journal of Algorithms
Approximation algorithms for multiple sequence alignment under a fixed evolutionary tree
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
The String-to-String Correction Problem
Journal of the ACM (JACM)
Topology of strings: median string is NP-complete
Theoretical Computer Science
The complexity of multiple sequence alignment with SP-score that is a metric
Theoretical Computer Science
A new algorithm for computing similarity between RNA structures
Information Sciences: an International Journal
A measure of discrepancy of multiple sequences
Information Sciences: an International Journal
A More Efficient Approximation Scheme for Tree Alignment
SIAM Journal on Computing
Theoretical Computer Science
Fundamentals of Data Structures in C++
Fundamentals of Data Structures in C++
Near optimal multiple alignment within a band in polynomial time
Journal of Computer and System Sciences
Multiple alignment by aligning alignments
Bioinformatics
Bioinformatics
Hi-index | 0.07 |
Given a set W of k sequences and a tree T with k leaves labeled with a unique sequence in W, a label tree is used to assign a sequence label to each internal node of the tree T. The cost of a tree edge is defined as the distance, such as the Hamming distance or the Levenshtein (edit) distance, between the sequence labels of a pair of nodes in the edge. The bottleneck edge of a label tree is the edge with the maximum cost in the label tree. The bottleneck tree alignment problem is concerned with the determination of a label tree with minimum cost of the bottleneck edge. A lifted label tree is a label tree in which the sequence label of each internal node is equal to the sequence label of some child of the node. The bottleneck lifted tree alignment problem involves the minimization of cost of the bottleneck edge among all possible lifted label trees of the tree T. This paper shows that when the distance function is a metric, the bottleneck tree alignment problem is NP-complete even when the tree structure resembles a binary tree. For special cases, an exact algorithm is used to solve the bottleneck lifted tree alignment problem in polynomial time. A 2(h-1)-approximation algorithm is used to solve the bottleneck tree alignment problem, where h is the height of the tree T. It is observed that the bound is existentially tight. Finally, this paper shows that any lifted label tree is an optimal solution to the bottleneck tree alignment problem if the distance function is an ultrametric.