The multiple sequence alignment problem in biology
SIAM Journal on Applied Mathematics
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximation algorithms for multiple sequence alignment
Theoretical Computer Science
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
Some open problems in computational molecular biology
ACM SIGACT News
A Polynomial-Time Approximation Scheme for Minimum Routing Cost Spanning Trees
SIAM Journal on Computing
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
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We consider a weighted generalization of multiple sequence alignment with sum-of-pair score. Multiple sequence alignment 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 can be approximated within a factor of O(log2 n) where n is the number of sequences. We prove that weighted multiple sequence alignment is MAX SNP-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 weighted multiple sequence alignment and its restriction to binary weights can be approximated exactly to the same degree.