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28
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.
Graph Sandwich Problems
, 1994
"... The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly o ..."
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Cited by 49 (8 self)
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The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly on properties characterizing subfamilies of perfect graphs, we give polynomial algorithms for several properties and prove the NPcompleteness of others. We describe
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.
A Geometric Approach to Betweenness
 IN PROCEEDINGS OF THE THIRD ANNUAL EUROPEAN SYMPOSIUM ALGORITHMS
, 1995
"... An input to the betweenness problem contains m constraints over n real variables. Each constraint consists of three variables, where one of the variables is specified to lie inside the interval defined by the other two. The order of the other two variables (which one is the largest and which one ..."
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Cited by 36 (1 self)
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An input to the betweenness problem contains m constraints over n real variables. Each constraint consists of three variables, where one of the variables is specified to lie inside the interval defined by the other two. The order of the other two variables (which one is the largest and which one is the smallest) is not specified. This problem comes up in questions related to physical mapping in computational molecular biology. In 1979, Opatrny has shown that the problem of deciding whether the n variables can be totally ordered while satisfying the m betweenness constraints is NP complete. Furthermore, the problem is MAX SNP complete. Therefore, there is some ffl ? 0 such that finding a total order which satisfies at least m(1 \Gamma ffl) of the constraints (even if they are all satisfiable) is NPhard. It is easy to find an ordering of the variables which satisfies 1=3 of the m constraints (e.g. by choosing the ordering at random). In this work we present a polynomial time algorithm which either determines that there is no feasible solution, or finds a total order which satisfies at least 1=2 of the m constraints. Our algorithm translates the problem into a set of quadratic inequalities, and solves a semidefinite relaxation of them in R n . The n solution points are then projected on a random line through the origin. Using simple geometric properties of the SDP solution, we prove the claimed performance guarantee.
Reasoning About Temporal Relations: The Tractable Subalgebras Of Allen's Interval Algebra
 Journal of the ACM
, 2001
"... Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra contains ex ..."
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Cited by 30 (2 self)
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Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra contains exactly eighteen maximal tractable subalgebras, and reasoning in any fragment not entirely contained in one of these subalgebras is NPcomplete. We obtain this result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using an algebraic technique for identifying maximal subalgebras with a given property.
A BranchandCut Approach to Physical Mapping of Chromosomes By Unique EndProbes
, 1997
"... A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 5276, 1995) first considered ..."
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Cited by 15 (5 self)
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A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 5276, 1995) first considered a maximumlikelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors, and developed several effective heuristics. We show that by exploiting information about the endprobes of clones, this model can be formulated as a weighted Betweenness Problem. This affords the significant advantage of allowing the welldeveloped tools of integer linearprogramming and branchandcut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness...
Multiniche crowding in genetic algorithms and its application to the assembly of DNA restrictionfragments
 Evolutionary Computation
, 1995
"... The determination of the sequence of all nucleotide basepairs in a DNA molecule, from restrictionfragment data, is a complex task and can be posed as the problem of finding the optima of a multimodal function. A genetic algorithm that uses multiniche crowding permits us to do this. Performance o ..."
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Cited by 14 (3 self)
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The determination of the sequence of all nucleotide basepairs in a DNA molecule, from restrictionfragment data, is a complex task and can be posed as the problem of finding the optima of a multimodal function. A genetic algorithm that uses multiniche crowding permits us to do this. Performance of this algorithm is first tested using a standard suite of test functions. The algorithm is next tested using two data sets obtained from the Human Genome Project at the Lawrence Livermore National Laboratory. The new method holds promise in automating the sequencing computations.
Ordinal embeddings of minimum relaxation: General properties, trees and ultrametrics
 Proceedings of the ACMSIAM Symposium on Discrete Algorithms
, 2005
"... We introduce a new notion of embedding, called minimumrelaxation ordinal embedding, parallel to the standard notion of minimumdistortion (metric) embedding. In an ordinal embedding, it is the relative order between pairs of distances, and not the distances themselves, that must be preserved as much ..."
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Cited by 10 (5 self)
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We introduce a new notion of embedding, called minimumrelaxation ordinal embedding, parallel to the standard notion of minimumdistortion (metric) embedding. In an ordinal embedding, it is the relative order between pairs of distances, and not the distances themselves, that must be preserved as much as possible. The (multiplicative) relaxation of an ordinal embedding is the maximum ratio between two distances whose relative order is inverted by the embedding. We develop several worstcase bounds and approximation algorithms on ordinal embedding. In particular, we establish that ordinal embedding has many qualitative differences from metric embedding, and capture the ordinal behavior of ultrametrics and shortestpath metrics of unweighted trees. 1
A BranchandCut Approach to Physical Mapping With EndProbes
, 1997
"... A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig [AKWZ94] first considered a maximumlikelihood model o ..."
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Cited by 10 (0 self)
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A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig [AKWZ94] first considered a maximumlikelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors, and developed several effective heuristics. We show that by exploiting information about the endprobes of clones, this model can be formulated as a weighted Betweenness Problem. This affords the significant advantage of allowing the welldeveloped tools of integer linearprogramming and branchandcut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness Problems, one can effectively...
Learning Multimodal Similarity
"... In many applications involving multimedia data, the definition of similarity between items is integral to several key tasks, including nearestneighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits multiple modalities, such as acoustic and visual content of ..."
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Cited by 8 (1 self)
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In many applications involving multimedia data, the definition of similarity between items is integral to several key tasks, including nearestneighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits multiple modalities, such as acoustic and visual content of video. Integrating such heterogeneous data to form a holistic similarity space is therefore a key challenge to be overcome in many realworld applications. We present a novel multiple kernel learning technique for integrating heterogeneous data into a single, unified similarity space. Our algorithm learns an optimal ensemble of kernel transformations which conform to measurements of human perceptual similarity, as expressed by relative comparisons. To cope with the ubiquitous problems of subjectivity and inconsistency in multimedia similarity, we develop graphbased techniques to filter similarity measurements, resulting in a simplified and robust training procedure.