The multiple sequence alignment problem in biology
SIAM Journal on Applied Mathematics
Multiple alignment, communication cost, and graph matching
SIAM Journal on Applied Mathematics
Aligning sequences via an evolutionary tree: complexity and approximation
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
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 Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
A polyhedral approach to sequence alignment problems
Discrete Applied Mathematics - Special volume on combinatorial molecular biology
A linear space algorithm for computing maximal common subsequences
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation Algorithms for Multiple Sequence Alignment
CPM '94 Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching
Improved Approximation Algorithms for Tree Alignment
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
CPM '98 Proceedings of the 9th Annual Symposium on Combinatorial Pattern Matching
The Maximum Weight Trace Problem in Multiple Sequence Alignment
CPM '93 Proceedings of the 4th Annual Symposium on Combinatorial Pattern Matching
Alignment between two multiple alignments
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
TreeRefiner: A Tool for Refining a Multiple Alignment on a Phylogenetic Tree
CSB '05 Proceedings of the 2005 IEEE Computational Systems Bioinformatics Conference
Learning Scoring Schemes for Sequence Alignment from Partial Examples
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Learning Models for Aligning Protein Sequences with Predicted Secondary Structure
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
MAUSA: using simulated annealing for guide tree construction in multiple sequence alignment
AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
Optimal global alignment of signals by maximization of Pearson correlation
Information Processing Letters
Simple and fast inverse alignment
RECOMB'06 Proceedings of the 10th annual international conference on Research in Computational Molecular Biology
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A basic computational problem that arises in both the construction and local-search phases of the best heuristics for multiple sequence alignment is that of aligning the columns of two multiple alignments. When the scoring function is the sum-of-pairs objective and induced pairwise alignments are evaluated using linear gap-costs, we call this problem Aligning Alignments. While seemingly a straightforward extension of two-sequence alignment, we prove it is actually NP-complete. As explained in the paper, this provides the first demonstration that minimizing linear gap-costs, in the context of multiple sequence alignment, is inherently hard.We also develop an exact algorithm for Aligning Alignments that is remarkably efficient in practice, both in time and space. Even though the problem is NP-complete, computational experiments on both biological and simulated data show we can compute optimal alignments for all benchmark instances in two standard datasets, and solve very-large random instances with highly-gapped sequences.