L. Goldstein and M. S. Waterman. Mapping DNA by stochastic relaxation. Advances in Applied Mathematics, 8:194--207, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the model of [22] for the special case of hybridization fingerprints with equal length clones. Using heuristics for a combinatorial version of the problem, they obtained encouraging results with simulated data. They also prove NP hardness of two variants of the problem. Goldstein and Waterman [15] have shown that restriction mapping is NP complete. In [14] two other models of physical mapping are shown to be NP complete: One model allows only false positive errors in determining intersections, and wishes to minimize their number. The other allows no errors but assumes that clones can ....

L. Goldstein and M. S. Waterman. Mapping DNA by stochastic relaxation. Advances in Applied Mathematics, 8:194--207, 1987.

....5 7 2 6 6 24 Figure 1: Example for the DOUBLE DGEST problem. Due to its importance in molecular biology, the DOUBLE DIGEST problem has been the subject of intense research since the first successful restriction site mappings in the early T970 s [16, 5] The DOUBLE DIGEST problem is NP complete [7], and several approaches including exponential algorithms, heuristics, additional experiments or computer assisted interactive strategies have been proposed (and implemented) in order to tackle the problem [3, T, 18, 8, 9] The number of feasible maps for a DOUBLE DIGEST instance can be ....

.... exponential algorithms, heuristics, additional experiments or computer assisted interactive strategies have been proposed (and implemented) in order to tackle the problem [3, T, 18, 8, 9] The number of feasible maps for a DOUBLE DIGEST instance can be exponential in the number of fragments [7]. However, some maps can be transformed into each other using cassette transformations [14] The set of different maps for an instance modulo cassette transformations can be characterized by using alternating Eulerian paths in appropriate graph classes [T0, TT] For a survey, see [17] and [12] ....

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L. Goldstein and M. S. Waterman. Mapping DNA by stochastic relaxation. Advaces i Applied Mathematics, 8:194 207, 1987.

....on a genome, was a critical component to early sequencing projects. For example, 9] provides a list of all restriction sites for the plasmid pBR322 under 81 di erent enzymes. Manyinteresting combinatorial and algorithmic problems have arisen in the context of technologies for restriction mapping [4,13, 19, 20]. Rebase [17] maintains a complete list of all known restriction enzymes, including cutter sequences, literature references, and commercial availability. AsofJanuary 1, 2001, 3487 di erent enzymes were known, de ning at least 255 distinct cutter sequences. Cutter sequence lengths range in length ....

L. Goldstein and M.S. Waterman. Mapping DNA by stochastic relaxation. Adv. in Applied Math., 8:194-207, 1987.

....in molecular biology labs for constructing the restriction maps for newly cloned DNA sequences. The problem can be difficult to solve, however, if the number of fragments is large. In general, it is intractable from the viewpoint of computational complexity as shown in Goldstein and Waterman [3]. Several approaches to the problem have been proposed, such as searching for all possible permutations [9, 11] simulated annealing [3, 4] and fragment matching [2, 7, 12] Software packages based on these approaches have been developed and used in practice [14] Moreover, in real applications, ....

....however, if the number of fragments is large. In general, it is intractable from the viewpoint of computational complexity as shown in Goldstein and Waterman [3] Several approaches to the problem have been proposed, such as searching for all possible permutations [9, 11] simulated annealing [3, 4], and fragment matching [2, 7, 12] Software packages based on these approaches have been developed and used in practice [14] Moreover, in real applications, the lengths of the DNA fragments are usually subject to measurement errors, and there are often multiple solutions to the double digestion ....

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L. Goldstein and M. S. Waterman, Mapping DNA by Stochastic Relaxation, Adv. Appl. Math., 8, 1987, pp. 194-207.

....with open problems in section 7. 2 Background and Previous Work Restriction mapping is a well studied problem in computational biology ( 17, 10] One of the rst attempts was the method of double digest ( 16] However it su ers from serious computational problems. Goldstein and Waterman [7] showed that it is NP complete. Further the number of possible solutions is exponential in the number of sites. Partial digest was proposed as an alternative technique, since the maximum number of solutions is smaller (only polynomial in the number of sites) from a combinatorial point of view it ....

L. Goldstein and M.S. Waterman. Mapping DNA by Stochastic Relaxation. Advances in Applied Mathematics, 8, 194-207, 1987.

....integers, containing exactly one zero. The reconstruction problem seeks all unordered pairs fX; Y g such that S = X Y = fx y : x 2 X; y 2 Y g. They prove that the number of solutions for a given set S can be Omega Gamma N 1:73 ) where N = jSj. In contrast, Goldstein and Waterman [8] showed that the number of solutions to a double digest problem can be exponential in the length of the segment. 4 3 The Reconstruction Algorithm The polynomial factorization approach does not generalize to noisy data, since it would require a concept analogous to an approximate factorization. ....

L. Goldstein and M.S. Waterman. Mapping dna by stochastic relaxation. Adv. in Applied Math., 8:194--207, 1987.

....bien la difficulte du probleme car le probleme de decision associe a DDP est NP complet 1 et il n existe donc probablement pas d algorithme permettant de resoudre ce probleme en temps polynomial dans le pire des cas. Dans la pratique, il est necessaire d enumerer exhaustivement les solutions et [GOL 87] ont montre que, pour ce probleme, le nombre de solutions crot en moyenne, et avec une probabilite de 1, de maniere exponentielle en fonction de la longueur du segment d ADN traite. Cependant, un nombre excessif de solutions est generalement sans interet et le probleme doit etre ( contraint ) ....

....traiter simultanement digestions partielles et doubles digestions completes. GA1 [STE 81] est un resolveur de 1: L appartenance a NP est immediate, la completude s obtient par restriction au probleme PARTITION correspondant aux cas ou l une des 2 enzymes produit deux segments de meme longueur [GOL 87] problemes sous contraintes dedie a la cartographie de restriction. Le probleme peut se modeliser dans le cadre CSP de la facon suivante : variables : a chaque fragment et site de coupure est associee une variable representant les positions possibles des fragments et sites de coupure ; ....

GOLDSTEIN L. et WATERMAN M., Mapping DNA by stochastic relaxation. Advances in Applied Mathematics, vol. 8, 1987, p. 194--207.

....heuristic approaches are needed to solve an instance of the problem in reasonable time. Simulated annealing [Churchill, Burks, Eggert, Engle, and Waterman, 1993) has been used for this problem as well as for the closely related physical map GENETIC ALGORITHMS FOR DNA SEQUENCING ping problem [Goldstein and Waterman, 1987)] Here we describe a genetic algorithm approach to the fragment assembly problem. The genetic algorithm is implemented within the context of the Genesis genetic algorithm package [Grefenstette, 1984) Our modifications to Genesis to support the new operators are all written in the C programming ....

L. Goldstein and M.S. Waterman. Mapping DNA by stochastic relaxation. Advances in Applied Mathematics, 8:194--207.

....reflects on the power of the mapping scheme to resolve ambiguities among maps; that is, a mapping scheme that yields many consistent maps may not be adequate. The question of multiplicity of solutions for other types of DNA mapping strategies has been previously addressed. Goldstein and Waterman [GW87] showed that if the enzyme sites are modeled as a Poisson process, then the Double Digest mapping problem can attain as many as an exponential number of solutions in the limit; these solutions have been further characterized by Schmitt and Waterman [SW91] The status of the question for Partial ....

Larry Goldstein and Michael S. Waterman. Mapping DNA by stochastic relaxation. Advances in Applied Mathematics, 8:194--207, 1987.

....enzyme map. It also reflects on the power of the mapping scheme to resolve ambiguities among maps; that is, a mapping scheme that yields many consistent maps may not be adequate. The question of multiplicity of solutions for other types of DNA mapping strategies has been previously addressed. It [GW87] it is shown that if the enzyme sites are modeled as a Poisson process, then the Double Digest 84 Mapping Problem can attain as many as an exponential number of solutions in the limit; these solutions have been further characterized in [SW91] The status of the question for (unprobed) Partial ....

Larry Goldstein and Michael S. Waterman. Mapping DNA by stochastic relaxation. Advances in Applied Mathematics, 8:194--207, 1987.

....the model of [35] for the special case of hybridization fingerprints with equal length clones. Using heuristics for a combinatorial version of the problem, they obtained encouraging results with simulated data. They also prove NPhardness of two variants of the problem. Goldstein and Waterman [20] show that restriction mapping is NP complete. These related hardness results are not equivalent to those presented here. 2 Colored Unit Interval Graph Completion Given a set of intervals on the real line, one can define a partial order on the intervals by a OE b if and only if the interval a is ....

L. Goldstein and M. S. Waterman. Mapping DNA by stochastic relaxation. Advances in Applied Mathematics, 8:194--207, 1987.

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L. Goldstein and M.S. Waterman. "Mapping DNA by Stochastic Relaxation," Adv. Appl. Math., 8:194--207, 1987.

No context found.

L. Goldstein and M.S. Waterman. Mapping DNA by stochastic Relaxation. Adv. Applied Math., 8(1987), 194--207.

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