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Haplotyping as Perfect Phylogeny: Conceptual Framework and Efficient Solutions (Extended Abstract)
, 2002
"... The next highpriority phase of human genomics will involve the development of a full Haplotype Map of the human genome [12]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A prototype Haplotype Mapping strat ..."
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Cited by 109 (10 self)
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The next highpriority phase of human genomics will involve the development of a full Haplotype Map of the human genome [12]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A prototype Haplotype Mapping strategy is presently being finalized by an NIH workinggroup. The biological key to that strategy is the surprising fact that genomic DNA can be partitioned into long blocks where genetic recombination has been rare, leading to strikingly fewer distinct haplotypes in the population than previously expected [12, 6, 21, 7]. In this paper
A lineartime algorithm for the perfect phylogeny haplotyping (PPH) problem
 In International Conference on Research in Computational Molecular Biology (RECOMB
, 2005
"... Since the introduction of the Perfect Phylogeny Haplotyping (PPH) Problem in RECOMB 2002 (Gusfield, 2002), the problem of finding a lineartime (deterministic, worstcase) solution for it has remained open, despite broad interest in the PPH problem and a series of papers on various aspects of it. In ..."
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Cited by 30 (8 self)
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Since the introduction of the Perfect Phylogeny Haplotyping (PPH) Problem in RECOMB 2002 (Gusfield, 2002), the problem of finding a lineartime (deterministic, worstcase) solution for it has remained open, despite broad interest in the PPH problem and a series of papers on various aspects of it. In this paper, we solve the open problem, giving a practical, deterministic lineartime algorithm based on a simple data structure and simple operations on it. The method is straightforward to program and has been fully implemented. Simulations show that it is much faster in practice than prior nonlinear methods. The value of a lineartime solution to the PPH problem is partly conceptual and partly for use in the inner loop of algorithms for more complex problems, where the PPH problem must be solved repeatedly. Key words: Perfect Phylogeny Haplotyping (PPH) Problem, Haplotype Inference Problem, lineartime algorithm, shadow tree. 1.
An Overview of Combinatorial Methods for Haplotype Inference
 Lecture Notes in Computer Science (2983): Computational Methods for SNPs and Haplotype Inference
, 2004
"... A current highpriority phase of human genomics involves the development of a full Haplotype Map of the human genome [23]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A key, perhaps bottleneck, problem is t ..."
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Cited by 23 (2 self)
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A current highpriority phase of human genomics involves the development of a full Haplotype Map of the human genome [23]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A key, perhaps bottleneck, problem is to computationally infer haplotype pairs from genotype data. This paper follows the talk given at the DIMACS Conference on SNPs and Haplotypes held in November of 2002. It reviews several combinatorial approaches to the haplotype inference problem that we have investigated over the last several years. In addition, it updates some of the work presented earlier, and discusses the current state of our work. 1 Introduction to SNP’s, Genotypes and Haplotypes In diploid organisms (such as humans) there are two (not completely identical) “copies ” of each chromosome, and hence of each region of interest.
Distance realization problems with applications to Internet tomography
"... In recent years, a variety of graph optimization problems have arisen in which the graphs involved are much too large for the usual algorithms to be effective. In these cases, even though we are not able to examine the entire graph (which may be changing dynamically), we would still like to deduce v ..."
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Cited by 13 (2 self)
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In recent years, a variety of graph optimization problems have arisen in which the graphs involved are much too large for the usual algorithms to be effective. In these cases, even though we are not able to examine the entire graph (which may be changing dynamically), we would still like to deduce various properties of it, such as the size of a connected component, the set of neighbors of a subset of vertices, etc. In this paper, we study a class of problems, called distance realization problems, which arise in the study of Internet data traffic models. uppose we are given a set S of terminal nodes, taken from some (unknown) weighted graph. A basic problem is to reconstruct a weighted graph G including S with possibly additional vertices, that realizes the given distance matrix for S. We will first show that this problem is not only difficult but the solution is often unstable in the sense that even if all distances between nodes in S decrease, the solution can increase by a factor proport...
A decomposition theory for binary linear codes,” submitted to
 IEEE Trans. Inform. Theory. ArXiv
"... ABSTRACT. The decomposition theory of matroids initiated by Paul Seymour in the 1980’s has had an enormous impact on research in matroid theory. This theory, when applied to matrices over the binary field, yields a powerful decomposition theory for binary linear codes. In this paper, we give an over ..."
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Cited by 7 (3 self)
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ABSTRACT. The decomposition theory of matroids initiated by Paul Seymour in the 1980’s has had an enormous impact on research in matroid theory. This theory, when applied to matrices over the binary field, yields a powerful decomposition theory for binary linear codes. In this paper, we give an overview of this code decomposition theory, and discuss some of its implications in the context of the recently discovered formulation of maximumlikelihood (ML) decoding of a binary linear code over a discrete memoryless channel as a linear programming problem. We translate matroidtheoretic results of Grötschel and Truemper from the combinatorial optimization literature to give examples of nontrivial families of codes for which the ML decoding problem can be solved in time polynomial in the length of the code. One such family is that consisting of codes C for which the codeword polytope is identical to the KoetterVontobel fundamental polytope derived from the entire dual code C ⊥. However, we also show that such families of codes are not good in a codingtheoretic sense — either their dimension or their minimum distance must grow sublinearly with codelength. 1.
Netform modeling and applications
 Interfaces
, 1990
"... Many realworld applications have profited from netform innovations in both modeling and solution strategies. Practical experience shoves that advances in netform modeling and solution strategies overcome many of the difficulties in conceptual design and problem solving of previous approaches to sys ..."
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Cited by 6 (0 self)
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Many realworld applications have profited from netform innovations in both modeling and solution strategies. Practical experience shoves that advances in netform modeling and solution strategies overcome many of the difficulties in conceptual design and problem solving of previous approaches to system optimization. Moreover, they provide the type of technologies required of truly useful decisionplanning tools, technologies that facilitate modeling, solution, and implementation. The ultimate test and worth of computerbased planning models, however, depends on their use by practitioners. In this tutorial, we show how certain algebraic models can be viewed graphically using netform modeling and describe several large practical problems we have solved. Some of our insights can make it easier for practitioners to take advantage of these technologies. The growth of the computer industry computer can record and manipulate exhas profoundly influenced many tremely large amounts of data. Without areas, affecting none more dramatically this capability, many of the tools of manthan management science. Knowledge agement science would be mere theoretical about ways to solve optimization problems niceties. in industry and government has exploded The techniques for building, solving, resince World War II, largely because the fining, and analyzing computerbased
Layering strategies for creating exploitable structure in linear and integer programs
 Mathematical Programming
, 1984
"... The strategy of subdividing optimization problems into layers by splitting variables into multiple copies has proved useful as a method for inducing exploitable structure in a variety of applications, particularly those involving embedded pure and generalized networks. A framework is proposed in thi ..."
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Cited by 5 (3 self)
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The strategy of subdividing optimization problems into layers by splitting variables into multiple copies has proved useful as a method for inducing exploitable structure in a variety of applications, particularly those involving embedded pure and generalized networks. A framework is proposed in this paper which leads to new relaxation and restriction methods for linear and integer programming based on our extension of this strategy. This framework underscores the use of constructions that lead to stronger relaxations and more flexible strategies than previous applications. Our results establish the equivalence of all layered Lagrangeans formed by parameterizing the equal value requirement of copied variables for different choices of the principal layers. It is further shown that these Lagrangeans dominate traditional Lagrangeans based on incorporating nonprincipal layers into the objective function. In addition a means for exploiting the layered Lagrangeans is provided by generating subgradients based on a simple averaging calculation. Finally, we show how this new layering strategy can be augmented by an integrated relaxation / restriction procedure, and indicate variations that can be employed to particular advantage in a parallel processing environment. Preliminary computational results on fifteen real world zeroone personnel assignment problems, comparing two layering approaches with five procedures previously found best for those problems, are encouraging. One of the layering strategies tested dominated all nonlayering procedures in terms of both quality and solution time.
A summary of Distance realization problems with applications to Internet tomography
"... we discuss here turn out to have a large numb er of applications in computationalb iology (e.g., constructing phylogenetic trees from genetic distances among living species), classification, etc. [1, 2, 13]. Here we will formulate several versions of this prob lem, mention the relevant result ..."
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we discuss here turn out to have a large numb er of applications in computationalb iology (e.g., constructing phylogenetic trees from genetic distances among living species), classification, etc. [1, 2, 13]. Here we will formulate several versions of this prob lem, mention the relevant results, b oth new and old, and discuss their algorithmic implications. First, we give some definitions. For a matrix D with rows and columns indexedb y S, we say D has a realization if there is a graph whose node set contains S,andD(u, v)isthe distanceb etween u and v. It is easy to see that a matrix D has a reali ation if its entries are nonnegative and satisfy the triangle inequality. D(u, v)+D(v,w) # D(u, w). (1) It turns out
DISCRETE ALGORITHMS FOR ANALYSIS OF GENOTYPE DATA
, 2007
"... Accessibility of highthroughput genotyping technology makes possible genomewide association studies for common complex diseases. When dealing with common diseases, it is necessary to search and analyze multiple independent causes resulted from interactions of multiple genes scattered over the enti ..."
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Accessibility of highthroughput genotyping technology makes possible genomewide association studies for common complex diseases. When dealing with common diseases, it is necessary to search and analyze multiple independent causes resulted from interactions of multiple genes scattered over the entire genome. The optimization formulations for searching diseaseassociated risk/resistant factors and predicting disease susceptibility for given casecontrol study have been introduced. Several discrete methods for disease association search exploiting greedy strategy and topological properties of casecontrol studies have been developed. New disease susceptibility prediction methods based on the developed search methods have been validated on datasets from casecontrol studies for several common diseases. Our experiments compare favorably the proposed algorithms with the existing association search and susceptibility prediction methods.