Abstract
This paper is concerned wth the physical mapping of DNA molecules using data about the hybridization of oligonucleotide probes to a library of clones. In mathematical terms, the DNA molecule corresponds to an interval on the real line, each clone to a subinterval, and each probe occurs at a finite set of points within the interval. A stochastic model for the occurrences of the probes and the locations of the clones is assumed. Given a matrix of incidences between probes and clones, the task is to reconstruct the most likely interleaving of the clones. Combinatorial algorithms are presented for solving approximations to this problem, and computational results are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Blum, T. Jiang, M. Li, J. Tromp, and M. Yannakakis. Linear approximation of shortest superstrings.Proceedings of the Twenty-Third Annual ACM Symposium on Theory of Computing, pp. 328–336, New Orleans, LA, May 1991. ACM Press, New York.
E. Branscomb, T. Slezak, R. Pae, D. Galas, A. V. Carrano, and M. Waterman. Optimizing restriction fragment fingerprinting methods for ordering large genomic libraries.Genomics,8(2), 351–366, October 1990.
A. V. Carrano, P. J. de Jong, E. Branscomb, T. Slezak, and B. Watkins. Constructing chromosome- and region-specific cosmid maps of the human genome.Genome,31(2), 1059–1065, 1989.
A. G. Craig, D. Nizetic, J. D. Hoheisel, G. Zehetner, and H. Lehrach. Ordering of cosmid clones covering the Herpes simplex virus type-I (HSV-I) genome-a test case for fingerprinting by hybridisation.Nucleic Acids Research,18(9), 2653–2660, May 11, 1990.
S. Lin and B. W. Kernighan. An effective heuristic algorithm for the traveling-salesman problem.Operations Research,21(2), March–April 1973.
E. S. Lander and M. S. Waterman. Genomic mapping by fingerprinting random clones: a mathematical analysis.Genomics,2(3), 231–239, April 1988.
K. Tynan, A. Olsen, B. Trask, P. de Jong, J. Thompson, W. Zimmermann, A. Carrano, and H. Mohrenweiser. Assembly and analysis of cosmid contigs in the CEA-gene family region of human chromosome 19.Nucleic Acids Research,20(7), 1629–1636, April 11, 1992.
J. S. Turner. Approximation algorithms for the shortest common superstring problem.Information and Computation,83(1), 1–20, October 1989.
Author information
Authors and Affiliations
Additional information
Communicated by E. W. Myers.
Research supported in part by NSF Grant No. CDA-9211106.
Research supported in part by NSF Grant No. CCR-9005448.
Rights and permissions
About this article
Cite this article
Alizadeh, F., Karp, R.M., Newberg, L.A. et al. Physical mapping of chromosomes: A combinatorial problem in molecular biology. Algorithmica 13, 52–76 (1995). https://doi.org/10.1007/BF01188581
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01188581