Results 1  10
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19
A Polyhedral Approach to RNA Sequence Structure Alignment
 Journal of Computational Biology
, 1998
"... Ribonucleic acid (RNA) is a polymer composed of four bases denoted A, C, G, and U. It generally is a singlestranded molecule where the bases form hydrogen bonds within the same molecule leading to structure formation. In comparing different homologous RNA molecules it is important to consider bo ..."
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Cited by 36 (4 self)
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Ribonucleic acid (RNA) is a polymer composed of four bases denoted A, C, G, and U. It generally is a singlestranded molecule where the bases form hydrogen bonds within the same molecule leading to structure formation. In comparing different homologous RNA molecules it is important to consider both the base sequence and the structure of the molecules. Traditional alignment algorithms can only account for the sequence of bases, but not for the base pairings. Considering the structure leads to significant computational problems because of the dependencies introduced by the base pairings. In this paper we address the problem of optimally aligning a given RNA sequence of unknown structure to one of known sequence and structure. We phrase the problem as an integer linear program and then solve it using methods from polyhedral combinatorics. In our computational experiments we could solve large problem instances  23S ribosomal RNA with more than 1400 bases  a size intractable f...
Modeling and Solving the Train Timetabling Problem
, 2000
"... The Train Timetabling Problem aims at determining a periodic timetable for a set of trains which does not violate track capacities and satises some operational constraints. In particular, we concentrate on the problem of a single, oneway track linking two major stations, with a number of interme ..."
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Cited by 18 (3 self)
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The Train Timetabling Problem aims at determining a periodic timetable for a set of trains which does not violate track capacities and satises some operational constraints. In particular, we concentrate on the problem of a single, oneway track linking two major stations, with a number of intermediate stations in between. Each train connects two given stations along the track (possibly dierent from the two major stations) and may have to stop for a minimum time in some of the intermediate stations. Trains can overtake each other only in correspondence of an intermediate station, and a minimum time interval between two consecutive departures and arrivals of trains in each station is specied. In this paper, we propose a graph theoretic formulation for the problem using a directed multigraph in which nodes correspond to departures/arrivals at a certain station at a given time instant. This formulation is used to derive an integer linear programming model which is relaxed in a Lagrangian way. A novel feature of our model is that the variables in the relaxed constraints are associated only with nodes (as opposed to arcs) of the aforementioned graph. This allows a considerable speedup in the solution of the relaxation. The relaxation is embedded within a heuristic algorithm which makes extensive use of the dual information associated with the Lagrangian multipliers. We report extensive computational results on realworld instances provided from Ferrovie dello Stato SpA, the Italian railway company, and from Ansaldo Segnalamento Ferroviario SpA.
The ABACUS System for BranchandCutandPrice Algorithms in Integer Programming and Combinatorial Optimization
, 1998
"... The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an objectoriented software framework for branchandcutandprice algorithms ..."
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Cited by 14 (0 self)
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The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an objectoriented software framework for branchandcutandprice algorithms for the solution of mixed integer and combinatorial optimization problems. This paper discusses some difficulties in the implementation of branchandcutandprice algorithms for combinatorial optimization problems and shows how they are managed by ABACUS.
Multiple sequence alignment with arbitrary gap costs: Computing an optimal solution using polyhedral combinatorics
, 2002
"... ..."
Multiple sequence alignment
 Protein Structure Prediction — Methods and Protocols
, 2000
"... Multiple sequence alignment is a central problem in Bioinformatics and a challenging one for optimisation algorithms. An established integer programming approach is to apply branchandcut to a graphtheoretical model. The models are exponentially large but are represented intensionally, and violate ..."
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Cited by 7 (1 self)
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Multiple sequence alignment is a central problem in Bioinformatics and a challenging one for optimisation algorithms. An established integer programming approach is to apply branchandcut to a graphtheoretical model. The models are exponentially large but are represented intensionally, and violated constraints can be located in polynomial time. This report describes a new integer program formulation that generates polynomialsized models small enough to be passed to generic solvers. It is a hybrid formulation relating the sparse alignment graph with a compact encoding of the alignment matrix via channelling constraints. Alignments obtained with a pseudoBoolean local search algorithm are competitive with those of stateoftheart algorithms. Execution times are much longer, but in future work we aim to develop a more efficient specialised algorithm. 1
Efficient Parameterized Algorithm for Biopolymer StructureSequence Alignment
 In Proceedings of Workshop on Algorithms for Bioinformatics
, 2005
"... Abstract. Computational alignment of a biopolymer sequence (e.g., an RNA or a protein) to a structure is an effective approach to predict and search for the structure of new sequences. To identify the structure of remote homologs, the structuresequence alignment has to consider not only sequence si ..."
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Cited by 7 (2 self)
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Abstract. Computational alignment of a biopolymer sequence (e.g., an RNA or a protein) to a structure is an effective approach to predict and search for the structure of new sequences. To identify the structure of remote homologs, the structuresequence alignment has to consider not only sequence similarity but also spatially conserved conformations caused by residue interactions, and consequently is computationally intractable. It is difficult to cope with the inefficiency without compromising alignment accuracy, especially for structure search in genomes or large databases. This paper introduces a novel method and a parameterized algorithm for structuresequence alignment. Both the structure and the sequence are represented as graphs, where in general the graph for a biopolymer structure has a naturally small tree width. The algorithm constructs an optimal alignment by finding in the sequence graph the maximum valued subgraph isomorphic to the structure graph. It has the computational time complexity O(k t N 2) for the structure of N residues and its tree decomposition of width t. The parameter k, small in nature, is determined by a statistical cutoff for the correspondence between the structure and the sequence. The paper demonstrates a successful application of the algorithm to developing a fast program for RNA structural homology search. 1
TwoLayer Planarization in Graph Drawing
 PROC. 9TH INTERNATIONAL SYMP. ON ALGORITHMS AND COMPUTATION (ISAAC'98), VOLUME 1533 OF LECTURE NOTES IN COMPUT. SCI
, 1998
"... 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 tw ..."
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Cited by 6 (0 self)
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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
A SATBased Approach to Multiple Sequence Alignment
 Poster, Ninth International Conference on Principles and Practice of Constraint Programming
, 2003
"... Abstract. Multiple sequence alignment is a central problem in Bioinformatics. A known integer programming approach is to apply branchandcut to exponentially large graphtheoretic models. This paper describes a new integer program formulation that generates models small enough to be passed to gener ..."
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Cited by 5 (3 self)
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Abstract. Multiple sequence alignment is a central problem in Bioinformatics. A known integer programming approach is to apply branchandcut to exponentially large graphtheoretic models. This paper describes a new integer program formulation that generates models small enough to be passed to generic solvers. The formulation is a hybrid relating the sparse alignment graph with a compact encoding of the alignment matrix via channelling constraints. Alignments obtained with a SATbased local search algorithm are competitive with those of stateoftheart algorithms, though execution times are much longer. 1
Protein Multiple Sequence Alignment
"... Protein sequence alignment is the task of identifying evolutionarily or structurally related positions in a collection of amino acid sequences. Although the protein alignment problem has been studied for several decades, many recent studies have demonstrated considerable progress in improving the ac ..."
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Cited by 3 (1 self)
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Protein sequence alignment is the task of identifying evolutionarily or structurally related positions in a collection of amino acid sequences. Although the protein alignment problem has been studied for several decades, many recent studies have demonstrated considerable progress in improving the accuracy or scalability of multiple and pairwise alignment tools, or in expanding the scope of tasks handled by an alignment program. In this chapter, we review stateoftheart protein sequence alignment and provide practical advice for users of alignment tools.
Computational Approaches to Problems in Protein Structure and Function
, 2005
"... We present computational approaches to solve several problems arising in protein structure and function. In the first part of this thesis, we develop a new method for finding the lowest energy positions of side chains when given the backbone of a protein, a widely studied problem that has applicatio ..."
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Cited by 1 (0 self)
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We present computational approaches to solve several problems arising in protein structure and function. In the first part of this thesis, we develop a new method for finding the lowest energy positions of side chains when given the backbone of a protein, a widely studied problem that has applications in homology modeling and protein design. We present an integer linear programming formulation of sidechain positioning and relax it to give a polynomialtime linear programming heuristic that allows us to tackle large problems. We test the integer and linear programming approach on native and homologous backbones, where we show that optimal solutions can usually be found using linear programming, and in protein redesign, where we find that instances often cannot be solved using linear programming directly, but where optimal solutions for large instances can be found using the more expensive integer programming procedure. We also present an alternative formulation of the sidechain positioning problem as a semidefinite program, which provides a tighter relaxation than the linear program. We introduce two novel rounding schemes to convert