The multiple sequence alignment problem in biology
SIAM Journal on Applied Mathematics
Mapping the genome: some combinatorial problems arising in molecular biology
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Approximation algorithms for multiple sequence alignment
Theoretical Computer Science
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
On approximation algorithms for local multiple alignment
RECOMB '00 Proceedings of the fourth annual international conference on Computational molecular biology
A Polynomial-Time Approximation Scheme for Minimum Routing Cost Spanning Trees
SIAM Journal on Computing
Some open problems in computational molecular biology
Journal of Algorithms
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
The complexity of multiple sequence alignment with SP-score that is a metric
Theoretical Computer Science
Some optimal inapproximability results
Journal of the ACM (JACM)
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Non-approximability of weighted multiple sequence alignment for arbitrary metrics
Information Processing Letters
Faster Algorithms for Optimal Multiple Sequence Alignment Based on Pairwise Comparisons
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Multiple Sequence Alignment as a Facility-Location Problem
INFORMS Journal on Computing
Non-approximability of weighted multiple sequence alignment for arbitrary metrics
Information Processing Letters
Multiple sequence alignment based on set covers
EuroGP'06 Proceedings of the 2006 international conference on Applications of Evolutionary Computing
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We consider a weighted generalization of multiple sequence alignment (MSA) with sum-of-pair score. MSA without weights is known to be NP-complete and can be approximated within a constant factor, but it is unknown whether it has a polynomial time approximation scheme. Weighted multiple sequence alignment (WMSA) can be approximated within a factor of O(log2n) where n is the number of sequences.We prove that WMSA alignment is MAX JNP-hard and establish a numerical lower bound on its approximability, namely 324/323 - ε This lower bound is obtained already for the simple binary weighted case where the weights are restricted to 0 and 1. Furthermore, we show that WMSA and its restriction to binary weights can be approximated to the same degree.