Abstract
The recent years have seen an impressive increase in the use of Integer Programming models for the solution of optimization problems originating in Molecular Biology. In this survey, some of the most successful Integer Programming approaches are described are described, while a broad overview of application areas being is given in modern Computational Molecular Biology.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Nemhauser G L, Wolsey L. Integer and Combinatorial Optimization. New York: John Wiley & Sons, 1988.
Cook W J, Cunningham W H, Pulleyblank W R, Schrijver A. Combinatorial Optimization. New York: John Wiley & Sons, 1998.
Schrijver A. Theory of Linear and Integer Programming. New York: John Wiley & Sons, 1986.
Reinert K, Lenhof H-P, Mutzel P, Mehlhorn K, Kececioglu J. A branch-and-cut algorithm for multiple sequence alignment. InProc. the Annual International Conference on Computational Molecular Biology (RECOMB), 1997, pp.241–249.
Kececioglu J, Lenhof H-P, Mehlhorn K, Mutzel P, Reinert K, Vingron M. A polyhedral approach to sequence alignment problems.Discrete Applied Mathematics, 2000, 104: 143–186.
Fischetti M, Lancia G, Serafini P. Exact algorithms for minimum routing cost trees.Networks, 2002, 39(3): 161–173.
Gusfield D. Efficient methods for multiple sequence alignment with guaranteed error bounds.Bulletin of Mathematical Biology, 1993, 55: 141–154.
Ben-Dor A, Lancia G, Perone J, Ravi R. Banishing bias from consensus sequences. InProc. the Annual Symposium on Combinatorial Pattern Matching (CPM), Lecture Notes in Computer Science 1264, 1997, pp.247–261.
Li M, Ma B, Wang L. On the closest string and substring problems.Journal of the ACM, 2002, 49(2): 157–171
Ma B. A polynomial time approximation scheme for the closest substring problem. InProc. the Annual Symposium on Combinatorial Pattern Matching (CPM), Lecture Notes in Computer Science 1848, 2000, pp.99–107.
Lanctot J, Li M, Ma Bet al. Distinguishing string selection problems. InProc. the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 1999, pp.633–642.
Lenhof H-P, Reinert K, Vingron M. A polyhedral approach to RNA sequence structure alignment.Journal of Computational Biology, 1998, 5(3): 517–530.
Lancia G, Carr R, Walenz Bet al. 101 optimal PDB structure alignments: A branch-and-cut algorithm for the maximum contact map overlap problem. InProceedings of the Annual International Conference on Computational Biology (RECOMB), 2001, pp.193–202.
Caprara A, Lancia G, Ng S K. A Column-Generation Based Branch-and-Bound Algorithm for Sorting by Reversal. InMathematical Support for Molecular Biology, Farach-Colton M, Roberts F S. Vingron M, Waterman M (Eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 1999, 47: 213–226.
Caprara A, Lancia G, Ng S K. Sorting permutations by reversals through branch and price.INFORMS Journal on Computing, 2001, 13(3): 224–244.
Lancia G, Bafna V, Istrail Set al. SNPs problems, complexity and algorithms. InProc. the Annual European Symposium on Algorithms (ESA), Lecture Notes in Computer Science 2161, 2001, pp.182–193.
Lippert R, Schwartz R, Lancia Get al. Algorithmic strategies for the SNPs haplotype assembly problem.Briefings in Bioinformatics, 2002, 3(1): 23–31.
Gusfield D. A practical algorithm for optimal inference of haplotypes from diploid populations. InProceedings of the Annual International Conference on Intelligent Systems for Molecular Biology (ISMB), 2000, pp.183–189.
Gusfield D. Inference of haplotypes from samples of diploid populations: Complexity and algorithms.Journal of Computational Biology, 2001, 8(3): 305–324.
Gusfield D. Haplotype inference by pure parsimony. Technical Report CSE-2003-2, Department of Computer Science, University of California at Davis, 2003.
Xu J, Li M, Kim Det al. RAPTOR: Optimal protein threading by linear programming.Journal of Bioinformatics and Computational Biology, 2003, 1(1): 95–117.
Christof T, Junger M, Kececioglu Jet al. A branch-and-cut approach to physical mapping with end-probes. InProc. the Annual International Conference on Computational Molecular Biology (RECOMB), 1997.
Agarwala R, Applegate D, Maglott Det al. A fast and scalable radiation hybrid map construction and integration strategy.Genome Research, 2000, 10: 230–364.
Kachian L G. A polynomial algorithms for linear programming.Soviet Mathematics Doklady, 1979, 20: 191–194.
Karmarkar N. A new polynomial time algorithm for linear programming.Combinatorica, 1984, 4: 375–395.
Grötschel M, Lovász L, Schrijver A. The ellipsoid method and its consequences in combinatorial optimization.Combinatorica, 1981, 1: 169–197.
Barnhart C, Johnson E L, Nemhauser G Let al. Branch-and-price: Column generation for solving hage integer programs.Operations Research, 1998, 46(3): 316–329.
Casey D. The Human Genome Project Primer on Molecular Genetics. U.S. Department of Energy, http://www.ornl.gov/hgmis/publicat/primer/intro. html, 1992.
Fitch W M. An Introduction to Molecular Biology for Mathematicians and Computer Programmers. InMathematical Support for Molecular Biology, Farach-Colton M, Roberts F S, Vingron M, Waterman M (Eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 1999, 47: 1–31.
Watson J D, Gilman M, Witkowski Jet al. Recombinant DNA. Scientific American Books, W. H. Freeman and Co, 1992.
Caprara A, Lancia G. Structural alignment of large-size proteins via Langragian relaxation. InProc. the Annual International Conference on Computational Molecular Biology (RECOMB), 2002, pp.100–108.
Needleman S B, Wunsch C D. An efficient method applicable to the search for similarities in the amino acid sequences of two proteins.Journal of Molecular Biology, 1970, 48: 443–453.
Wang L, Jiang T. On the complexity of multiple sequence alignment.Journal of Computational Biology, 1994, 1: 337–348.
Sankoff D, Kruskal J. Time Warps, String Edits, and Macromolecules: The Theory and Practice of String Comparison. CSLI Publications, 1999.
Kececioglu J. The maximum weight trace problem in multiple sequence alignment. InProc. the Annual Symposium on Combinatorial Pattern Matching (CPM), Lecture Notes in Computer Science 684, 1993, pp.106–119.
Wu B Y, Lancia G, Bafna Vet al. A polynomial-time approximation scheme for minimum routing cost spaning trees.SIAM Journal on Computing, 1999, 29(3): 761–778.
Frances M, Litman A. On covering problems of codes.Theory of Computing Systems, 1997, 30(2): 113–119.
Raghavan P, Thompson C D. Randomized rounding: A technique for provably good algorithms and algorithmic proofs.Combinatorica, 1987, 7: 365–374.
Raghavan P. A probabilistic construction of deterministic algorithms: Approximating packing integer programs.Journal of Computer and System Sciences, 1988, 37: 130–143.
Lemmen C, Lengauer T. Computational methods for the structural alignment of molecules.Journal of Computer-Aided Molecular Design, 2000, 14: 215–232.
Berman H M, Westbrook J, Feng Zet al. The protein data bank.Nuclic Acids Research, 2000, 28: 235–242.
Goldman D, Istrail S, Papadinitriou C. Algorithmic aspects of protein structure similarity. InProc. the Annual IEEE Symposium on Foundations of Computer Science (FOCS), 1999, pp.512–522.
Godzik A, Skolnick J, Kolinski A. A topology fingerprint approach to inverse protein folding problem.Journal of Molecular Biology, 1992, 227: 227–238.
Bafna V, Pevzner P A. Genome rearrangements and sorting by reversals.SIAM Journal on Computing, 1996, 25: 272–289.
Caprara A. On the tightness of the alternating-cycle lower bound for sorting by reversals.Journal of Combinatorial Optimization, 1999, 3: 149–182.
Caprara A. Sorting permutations by reversals and Eulerian cycle decompositions.SIAM Journal on Discrete Mathematics, 1999, 12: 91–110.
Grötschel M, Pulleyblank W R. Weakly bipartite graphs and the max-cut problem.Operations Research Letters, 1981, 1: 23–27.
Clark A. Inferences of haplotype from PCR-amplified samples of diploid populations.Molecular Biology Evolution, 1990, 7: 111–122.
Lancia G, Pinotti C, Rizzi R. Haplotyping populations: Complexity, and approximations. Technical Report, University of Trento, 2002.
Applegate D, Bixby R, Chvatal Vet al. CONCORDE: A code for solving traveling salesman problems. http://www.math.princeton.edu/tsp/concorde.html
Author information
Authors and Affiliations
Corresponding author
Additional information
Giuseppe Lancia is an associate professor in operations research at the University of Udine, Italy. He holds the M.S. and the Ph.D. degrees in algorithms, combinatorics and optimization from Carnegie Mellon University, USA. His research interests include combinatorial optimization, mathematical programming, and discrete mathematics, with a special emphasis on their applications to computational molecular biology problems. In this field. Giuseppe Lancia has authored some 30 papers. He has been a member of the program committee of prestigious conferences such as RECOMB and WABI and a co-editor of a special issue of the INFORMS Journal on Computing. Furthermore, he has spent extended periods as a visiting scientist at Sandia National Labs, Albuquerque NM, and Celera Genomics, Rockville MD, working on computational biology problems related to SNPs genotyping, protein structure analysis, sequence alignment, and genome rearrangements.
Rights and permissions
About this article
Cite this article
Lancia, G. Integer programming models for computational biology problems. J. Comput. Sci. & Technol. 19, 60–77 (2004). https://doi.org/10.1007/BF02944785
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02944785