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Four Strikes against Physical Mapping of DNA
 JOURNAL OF COMPUTATIONAL BIOLOGY
, 1993
"... Physical Mapping is a central problem in molecular biology ... and the human genome project. The problem is to reconstruct the relative position of fragments of DNA along the genome from information on their pairwise overlaps. We show that four simplified models of the problem lead to NPcomplete ..."
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Cited by 55 (8 self)
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Physical Mapping is a central problem in molecular biology ... and the human genome project. The problem is to reconstruct the relative position of fragments of DNA along the genome from information on their pairwise overlaps. We show that four simplified models of the problem lead to NPcomplete decision problems: Colored unit interval graph completion, the maximum interval (or unit interval) subgraph, the pathwidth of a bipartite graph, and the kconsecutive ones problem for k >= 2. These models have been chosen to reflect various features typical in biological data, including false negative and positive errors, small width of the map and chimericism.
On the Complexity of DNA Physical Mapping
, 1994
"... 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 NPcomplete problems, which are conjectured to be computationa ..."
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Cited by 41 (7 self)
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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 NPcomplete 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.
Genomic Mapping by End Characterized Random Clones: A Mathematical Analysis
 Genomics
, 1995
"... Physical maps can be constructed by "fingerprinting" a large number of random clones and inferring overlap between clones when the fingerprints are su#ciently similar. Lander and Waterman (Genomics (1988) 2: 231239) gave a mathematical analysis of such mapping strategies. The analysis is useful for ..."
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Cited by 5 (0 self)
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Physical maps can be constructed by "fingerprinting" a large number of random clones and inferring overlap between clones when the fingerprints are su#ciently similar. Lander and Waterman (Genomics (1988) 2: 231239) gave a mathematical analysis of such mapping strategies. The analysis is useful for comparing various fingerprinting methods. Recently it has been proposed to fingerprint or characterize ends of clones rather than the entire clone. Such fingerprints, which include sequenced clone ends, require a deeper mathematical analysis than that of LanderWaterman. This paper studies clone islands, which can include uncharacterized regions, and also the islands that are formed entirely from the ends of clones. 1 1
Beyond Islands: Runs in CloneProbe Matrices (extended abstract)
 Proceedings of the 1st ACM Conference on Computational Molecular Biology, 320329
, 1997
"... Physical mapping is a fundamental component of the human genome project. A physical map consists of a set of probes which mark unique positions on a long fragment of DNA, together with the relative order of the probes on the DNA. This order is inferred from cloneprobe hybridization experiments, whi ..."
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Cited by 3 (0 self)
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Physical mapping is a fundamental component of the human genome project. A physical map consists of a set of probes which mark unique positions on a long fragment of DNA, together with the relative order of the probes on the DNA. This order is inferred from cloneprobe hybridization experiments, which determine the probes contained within various fragments of the genome. In practice, the order of the probes is not completely determined by the hybridization experiments. To better design these experiments, researchers have analyzed the expected distribution of "islands"  groups of probes which are known to be near one another  that would result from hybridization experiments with different numbers of clones and probes. In this paper we analyze the distribution of "runs"  groups of probes whose relative order is completely determined by the hybridization experiment. We include analytic, numerical, Monte Carlo, and simulation results on runs, which can further assist in the design...
Using nonhomogeneous processes in physical mapping by anchoring random clones: Mathematical analysis and application to hotspots.
, 1996
"... The aim of this report is to provide general results for predicting progress in a physical mapping project by anchoring random clones, when clones and anchors are not homogeneously distributed along the genome. A complete physical map of the DNA of an organism consists of overlapping clones spanning ..."
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Cited by 1 (1 self)
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The aim of this report is to provide general results for predicting progress in a physical mapping project by anchoring random clones, when clones and anchors are not homogeneously distributed along the genome. A complete physical map of the DNA of an organism consists of overlapping clones spanning the entire genome. Several schemes can be used to construct such a map, depending on the way that clones overlap. We focus here on the approach consisting of assembling clones sharing a common random short sequence called an anchor. Some mathematical analyses providing statistical properties of anchored clones have been developed in the stationary case. Modeling the clone and anchor processes as nonhomogeneous Poisson processes provides such an analysis in a general nonstationary framework. We apply our results to a natural nonhomogeneous model to illustrate the effect of inhomogeneity. This model reflects clone and anchor hotspots. This study reveals that using homogeneous processes for...
Coverage Processes in Physical Mapping by Anchoring Random Clones
 J. Comp. Biol
, 1997
"... this paper is to provide a mathematical analysis of physical mapping by anchoring random clones, in a general model. ..."
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this paper is to provide a mathematical analysis of physical mapping by anchoring random clones, in a general model.
BMC Genomics BioMed Central
, 2009
"... Research article Statistical aspects of discerning indeltype structural variation via DNA sequence alignment ..."
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Research article Statistical aspects of discerning indeltype structural variation via DNA sequence alignment