TY - GEN

T1 - Hardness and approximation of the asynchronous border minimization problem

AU - Popa, Alexandru

AU - Wong, Prudence W.H.

AU - Yung, Fencol C.C.

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2012

Y1 - 2012

N2 - 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 log 2 n) to O(n 1/4 log 2n), where n is the total number of sequences.

AB - 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 log 2 n) to O(n 1/4 log 2n), where n is the total number of sequences.

UR - http://www.scopus.com/inward/record.url?scp=84861000931&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-29952-0_20

DO - 10.1007/978-3-642-29952-0_20

M3 - Conference contribution

AN - SCOPUS:84861000931

SN - 9783642299513

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 164

EP - 176

BT - Theory and Applications of Models of Computation - 9th Annual Conference, TAMC 2012, Proceedings

T2 - 9th Annual Conference on Theory and Applications of Models of Computation, TAMC 2012

Y2 - 16 May 2012 through 21 May 2012

ER -