On the Complexity of DNA Physical Mapping

The physical mapping problem is to reconstruct the relative position of fragments (clones) of DNA along the genome from information on their pairwise overlaps. We show that two simplified versions of the problem belong to the class of NP-complete problems, which are conjectured to be computationally intractable. In one version all clones have equal length, and in another clone lengths may be arbitrary. The proof uses tools from graph theory and complexity.

[1]  S. Benzer.  ON THE TOPOLOGY OF THE GENETIC FINE STRUCTURE. , 1959, Proceedings of the National Academy of Sciences of the United States of America.

[2]  D. Nathans,et al.  Studies of simian virus 40 DNA. VII. A cleavage map of the SV40 genome. , 1973, Journal of molecular biology.

[3]  Thomas J. Schaefer,et al.  The complexity of satisfiability problems , 1978, STOC.

[4]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5]  Jaroslav Opatrny,et al.  Total Ordering Problem , 1979, SIAM J. Comput..

[6]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[7]  M. Olson,et al.  Random-clone strategy for genomic restriction mapping in yeast. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Jerrold R. Griggs,et al.  Interval graphs and maps of DNA , 1986 .

[9]  A. Coulson,et al.  Toward a physical map of the genome of the nematode Caenorhabditis elegans. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[10]  M. Olson,et al.  Cloning of large segments of exogenous DNA into yeast by means of artificial chromosome vectors. , 1987, Science.

[11]  Hans Lehrach,et al.  Molecular approaches to genome analysis: a strategy for the construction of ordered overlapping clone libraries , 1987, Comput. Appl. Biosci..

[12]  K. Isono,et al.  The physical map of the whole E. coli chromosome: Application of a new strategy for rapid analysis and sorting of a large genomic library , 1987, Cell.

[13]  M. Waterman,et al.  Mapping DNA by stochastic relaxation , 1987 .

[14]  A. Coulson,et al.  Genome linking with yeast artificial chromosomes , 1988, Nature.

[15]  E. Lander,et al.  Genomic mapping by fingerprinting random clones: a mathematical analysis. , 1988, Genomics.

[16]  A. Carrano.  Establishing the order of human chromosome-specific DNA fragments. , 1988, Basic life sciences.

[17]  U. S. Congress.  Mapping Our Genes: Genome Projects--How Big, How Fast? , 1988 .

[18]  L. Hood,et al.  A common language for physical mapping of the human genome. , 1989, Science.

[19]  H. Lehrach,et al.  Ordering of cosmid clones covering the herpes simplex virus type I (HSV-I) genome: a test case for fingerprinting by hybridisation. , 1990, Nucleic acids research.

[20]  N. Sternberg,et al.  Bacteriophage P1 cloning system for the isolation, amplification, and recovery of DNA fragments as large as 100 kilobase pairs. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Dale H. Cowan.  Mapping Our Genes: Genome Projects: How Big, How Fast? , 1990 .

[22]  G Hermanson,et al.  High-resolution mapping of human chromosome 11 by in situ hybridization with cosmid clones. , 1990, Science.

[23]  M. Olson,et al.  Chromosomal region of the cystic fibrosis gene in yeast artificial chromosomes: a model for human genome mapping. , 1990, Science.

[24]  E. Lander,et al.  Genomic mapping by anchoring random clones: a mathematical analysis. , 1991, Genomics.

[25]  J Dausset,et al.  Theoretical analysis of a physical mapping strategy using random single-copy landmarks. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Sampath Kannan,et al.  Triangulating 3-Colored Graphs , 1992, SIAM J. Discret. Math..

[27]  Michael R. Fellows,et al.  Two Strikes Against Perfect Phylogeny , 1992, ICALP.

[28]  B. Trask,et al.  Assembly and analysis of cosmid contigs in the CEA-gene family region of human chromosome 19. , 1992, Nucleic acids research.

[29]  Ron Shamir,et al.  Complexity and algorithms for reasoning about time: a graph-theoretic approach , 1993, JACM.

[30]  Lee Aaron Newberg,et al.  Physical mapping of chromosomes: A combinatorial problem in molecular biology , 1995, SODA '93.

[31]  Michael R. Fellows,et al.  DNA Physical Mapping: Three Ways Difficult , 1993, ESA.

[32]  Martin Charles Golumbic,et al.  Graph Sandwich Problems , 1995, J. Algorithms.