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Approximating Border Length for DNA Microarray Synthesis
"... Abstract. We study the border minimization problem (BMP), which arises in microarray synthesis to place and embed probes in the array. The synthesis is based on a lightdirected chemical process in which unintended illumination may contaminate the quality of the experiments. Border length is a measu ..."
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Abstract. We study the border minimization problem (BMP), which arises in microarray synthesis to place and embed probes in the array. The synthesis is based on a lightdirected chemical process in which unintended illumination may contaminate the quality of the experiments. Border length is a measure of the amount of unintended illumination and the objective of BMP is to find a placement and embedding of probes such that the border length is minimized. The problem is believed to be NPhard. In this paper we show that BMP admits an O ( √ nlog 2 n)approximation, where n is the number of probes to be synthesized. In the case where the placement is given in advance, we show that the problem is O(log 2 n)approximable. We also study a related problem called agreement maximization problem (AMP). In contrast to BMP, we show that AMP admits a constant approximation even when placement is not given in advance. 1
A BranchandCut Algorithm for Multiple Sequence Alignment
"... Abstract. We consider a branchandcut approach for solving the multiple sequence alignment problem, which is a central problem in computational biology. We propose a general model for this problem in which arbitrary gap costs are allowed. An interesting aspect of our approach is that the three (exp ..."
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Abstract. We consider a branchandcut approach for solving the multiple sequence alignment problem, which is a central problem in computational biology. We propose a general model for this problem in which arbitrary gap costs are allowed. An interesting aspect of our approach is that the three (exponentially large) classes of natural valid inequalities that we consider turn out to be both facetdefining for the convex hull of integer solutions and separable in polynomial time. Both the proofs that these classes of valid inequalities are facetdefining and the description of the separation algorithms are far from trivial. Experimental results on several benchmark instances show that our method outperforms the best tools developed so far, in that it produces alignments that are better from a biological point of view. A noteworthy outcome of the results is the effectiveness of using branchandcut with only a carefullyselected subset of the variables as a heuristic. 1.
BIOINFORMATICS ORIGINAL PAPER Structural bioinformatics
, 2004
"... Extracting multiple structural alignments from pairwise alignments: a comparison of a rigorous and a heuristic approach ..."
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Extracting multiple structural alignments from pairwise alignments: a comparison of a rigorous and a heuristic approach
TwoLayer Planarization in Graph Drawing (Extended Abstract)
, 1998
"... ) Abstract We study the twolayer planarization problems that have applications in Automatic Graph Drawing. We are searching for a twolayer planar subgraph of maximum weight in a given twolayer graph. Depending on the number of layers in which the vertices can be permuted freely, that is, zero, o ..."
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) Abstract We study the twolayer planarization problems that have applications in Automatic Graph Drawing. We are searching for a twolayer planar subgraph of maximum weight in a given twolayer graph. Depending on the number of layers in which the vertices can be permuted freely, that is, zero, one or two, different versions of the problems arise. The latter problem was already investigated in [11] using polyhedral combinatorics. Here, we study the remaining two cases and the relationships between the associated polytopes. In particular, we investigate the polytope P 1 associated with the twolayer planarization problem with one fixed layer. We provide an overview on the relationships between P 1 and the polytope Q 1 associated with the twolayer crossing minimization problem with one fixed layer, the linear ordering polytope, the twolayer planarization problem with zero and two layers fixed. We will see that all facetdefining inequalities in Q 1 are also facetdefining for P 1 ...
Algorithms on Constrained Sequence Alignment
, 2004
"... One of the fundamental issues that arises in computational biology is Multiple Sequence Alignment (MSA), which needs to be addressed in many applications of Bioinformatics (e.g. study of the SARS Coronavirus and the Human Genome Project). Many algorithms have been proposed to solve the MSA problem, ..."
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One of the fundamental issues that arises in computational biology is Multiple Sequence Alignment (MSA), which needs to be addressed in many applications of Bioinformatics (e.g. study of the SARS Coronavirus and the Human Genome Project). Many algorithms have been proposed to solve the MSA problem, but often cannot incorporate users' (biologists') knowledge of the functionalities or structures of these sequences into their solutions. This kind of information is very useful for an accurate and biologically meaningful alignment. The Constrained Multiple Sequence Alignment (CMSA) was proposed by Tang et al. (2002) to rectify the shortcomings of MSA by introducing a constrained sequence to represent more important residues in the sequences. Every character of the constrained sequence has to appear in an entire column in the alignment of the multiple sequences, and in the same order as in the constrained sequence.
Optimization Problems in Molecular Biology: A Survey and Critical Review
"... Computational molecular biology has emerged as one of the most exciting interdisciplinary fields, riding on the success of the ongoing Human Genome Project, which culminated in the 2001 announcement of the complete sequencing of the human genome. It is only in the past few years that it has been sho ..."
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Computational molecular biology has emerged as one of the most exciting interdisciplinary fields, riding on the success of the ongoing Human Genome Project, which culminated in the 2001 announcement of the complete sequencing of the human genome. It is only in the past few years that it has been shown that a large number of molecular biology problems can be formulated as combinatorial optimization problems, including sequence alignment problems, genome rearrangement problems, string selection and comparison problems, and protein structure prediction and recognition. This paper provides a detailed description of several interesting molecular biology problems that can be formulated as combinatorial optimization problems and surveys the most efficient stateoftheart techniques and algorithms to exactly or approximately solve them.
Hardness and Approximation of The Asynchronous Border Minimization Problem
"... Abstract. 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 pro ..."
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Abstract. 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 PBMP, 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 NPhard or not. In this paper, we give a comprehensive study of different variations of BMP by presenting NPhardness proofs and improved approximation algorithms. We show that PBMP, 1DBMP, and BMP are all NPhard. In contrast with the result in [21] that 1DPBMP is polynomial time solvable, the interesting implications include (i) the array dimension (1D or 2D) differentiates the complexity of PBMP; (ii) for 1D array, whether placement is given differentiates the complexity of BMP; (iii) BMP is NPhard 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 2 n), where n is the total number of sequences. 1
UTILISATION DES ALGORITHMES GENETIQUES POUR L’ANALYSE DE SEQUENCES BIOLOGIQUES
"... I wish to thank the EMBL for their funding through an EMBL grant. This work was carried out in the lab of Des Higgins, first at the European Molecular Biology Laboratory in Heidelberg,Germany and later at the EMBL outstation, the European Bioinformatics Institute, in Hinxton, U.K. Des has been a con ..."
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I wish to thank the EMBL for their funding through an EMBL grant. This work was carried out in the lab of Des Higgins, first at the European Molecular Biology Laboratory in Heidelberg,Germany and later at the EMBL outstation, the European Bioinformatics Institute, in Hinxton, U.K. Des has been a constant source of support. I wish to thank him and express him all my gratitude for teaching me most of what I know in bioinformatics, and so much more about being a scientist. I also wish to thank Ture Etzold who gave me a place in his team when Des had to leave for Ireland. Thanks to his expertise in the field, Thure has had a lots of influence on my work. A special thanks to the system managers, namely Roy Omond, Rodrigo Lopez and Pettere Jokinen who have always been supportive, allowing me to overload the machines any time I needed it. Without their help, this work could not have been achieved. I also wish to thank Miguel Andrade, Inge Jonassen and Burkhard Rost for stimulating discussions and frendship. Chris Sander and Liisa Holm have always been available to share with me their extensive experience of the field. I wish to