Approximation algorithms for multiple sequence alignment
Theoretical Computer Science
A branch-and-cut algorithm for multiple sequence alignment
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
Class prediction and discovery using gene expression data
RECOMB '00 Proceedings of the fourth annual international conference on Computational molecular biology
The complexity of multiple sequence alignment with SP-score that is a metric
Theoretical Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Fast and Accurate Probe Selection Algorithm for Large Genomes
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
On the Hardness of the Border Length Minimization Problem
BIBE '09 Proceedings of the 2009 Ninth IEEE International Conference on Bioinformatics and Bioengineering
Approximating border length for DNA microarray synthesis
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Improving the layout of oligonucleotide microarrays: pivot partitioning
WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
Computer-Aided Optimization of DNA Array Design and Manufacturing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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We study a combinatorial problem arising from the microarrays synthesis. The objective of the BMP is to place a set of sequences in the array and to find an embedding of these sequences into a common supersequence such that the sum of the "border length" is minimized. A variant of the problem, called P-BMP, is that the placement is given and the concern is simply to find the embedding. Approximation algorithms have been proposed for the problem [21] but it is unknown whether the problem is NP-hard or not. In this paper, we give a comprehensive study of different variations of BMP by presenting NP-hardness proofs and improved approximation algorithms. We show that P-BMP, 1D-BMP, and BMP are all NP-hard. In contrast with the result in [21] that 1D-P-BMP is polynomial time solvable, the interesting implications include (i) the array dimension (1D or 2D) differentiates the complexity of P-BMP; (ii) for 1D array, whether placement is given differentiates the complexity of BMP; (iii) BMP is NP-hard regardless of the dimension of the array. Another contribution of the paper is improving the approximation for BMP from O (n 1/2 log2n ) to O (n 1/4 log2n ), where n is the total number of sequences.