Trees, stars, and multiple biological sequence alignment
SIAM Journal on Applied Mathematics
On better heuristic for euclidean Steiner minimum trees (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Improved approximations for the Steiner tree problem
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Aligning sequences via an evolutionary tree: complexity and approximation
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Algorithms for Enumerating All Spanning Trees ofUndirected and Weighted Graphs
SIAM Journal on Computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Improved approximation algorithms for tree alignment
Journal of Algorithms
The deferred path heuristic for the generalized tree alignment problem
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
A More Efficient Approximation Scheme for Tree Alignment
SIAM Journal on Computing
Better approximation bounds for the network and Euclidean Steiner tree problems
Better approximation bounds for the network and Euclidean Steiner tree problems
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In generalized tree alignment problem, we are given a set S of k biologically related sequences and we are interested in a minimum cost evolutionary tree for S. In many instances of this problem partial phylogenetic tree for S is known. In such instances, we would like to make use of this knowledge to restrict the tree topologies that we consider and construct a biologically relevant minimum cost evolutionary tree. So, we propose the following natural generalization of the generalized tree alignment problem, a problem known to be MAX-SNP Hard, stated as follows: Constrained Generalized Tree Alignment Problem [S. Divakaran, Algorithms and heuristics for constrained generalized alignment problem, DIMACS Technical Report 2007-21, 2007]: Given a set S of k related sequences and a phylogenetic forest comprising of node-disjoint phylogenetic trees that specify the topological constraints that an evolutionary tree of S needs to satisfy, construct a minimum cost evolutionary tree for S. In this paper, we present constant approximation algorithms for the constrained generalized tree alignment problem. For the generalized tree alignment problem, a special case of this problem, our algorithms provide a guaranteed error bound of 2-2/k.