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Genomics via Optical Mapping III: Contiging Genomic DNA and Variations (Extended Abstract)
, 1997
"... ) Thomas Anantharaman, Bud Mishra and David Schwartz 1 Abstract In this paper, we describe our algorithmic approach to constructing an alignment of (con tiging) a set of optical maps created from the images of individual genomic DNA molecules digested by restriction enzymes. Generally, these DNA ..."
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Cited by 26 (19 self)
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) Thomas Anantharaman, Bud Mishra and David Schwartz 1 Abstract In this paper, we describe our algorithmic approach to constructing an alignment of (con tiging) a set of optical maps created from the images of individual genomic DNA molecules digested by restriction enzymes. Generally, these DNA segments are sized in the range of 14Mb. The problem of assembling clone contig maps is a simpler special case of this contig problem and is handled by our algorithms. The goal is to devise contiging algorithms capable of producing highquality composite maps rapidly and in a scalable manner. The resulting software is a key component of our physical mapping automation tools and has been used routinely to create composite maps of various microorganisms (E. coli, P. falciparum and D. radioduran). The experimental results appear highly promising. 1 Introduction Single molecule approaches provide a new direction for characterizing structural and functional properties of individual DNA molec...
Rapid DNA mapping by fluorescent single molecule detection
 Nucleic Acids Res
, 2007
"... doi:10.1093/nar/gkl1044 ..."
A Probabilistic Analysis of False Positives in Optical Map Alignment and Validation
 Algorithms in Bioinformatics, First International Workshop, WABI 2001 Proceedings LNCS 2149
, 2001
"... this paper, we explicitly delineate the interdependencies among these parameters and explore the tradeo#s in parameter space: e.g., sizing error vs. digestion rate vs. total coverage. 1.1 Summary of the Main Results ..."
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Cited by 5 (3 self)
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this paper, we explicitly delineate the interdependencies among these parameters and explore the tradeo#s in parameter space: e.g., sizing error vs. digestion rate vs. total coverage. 1.1 Summary of the Main Results
Genomics via Optical Mapping IV: Sequence Validation via Optical Map Matching
, 2001
"... This paper describes the underlying mathematical model and the dynamic programming algorithm technology for the validation of a (DNA) sequence against a (DNA) map. The sequence can be obtained from a variety of sources (e.g. GenBank, Sanger's Lab, or Celera P.E.) and it is assumed to be written out ..."
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Cited by 5 (3 self)
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This paper describes the underlying mathematical model and the dynamic programming algorithm technology for the validation of a (DNA) sequence against a (DNA) map. The sequence can be obtained from a variety of sources (e.g. GenBank, Sanger's Lab, or Celera P.E.) and it is assumed to be written out as a string of nucleotides. The map is an ordered restriction map obtained through an optical mapping process and is augmented with statistical information which will be used to place (or not) the sequence in the genome. Our approach has many other applications beyond validation: e.g. mapbased sequence assembly, phasing sequence contigs, detecting and closing gaps and annotation of partially sequenced genomes to nd open reading frames, genes, and synteny groups. We tested our system by checking various maps against publicly available sequence data for Plasmodium falciparum (cf. [10, 11]). 1 Object Denitions and Processes Denitions The objects we will be dealing with in the following are...
Genomics via Optical Mapping II(A): Restriction Maps from Partial Molecules and Variations (Extended Abstract)
 Courant Institute of Mathematical Sciences
, 1996
"... ) Thomas Anantharaman and Bud Mishra 1 Abstract In this paper, we extend an algorithmic approach to constructing ordered restriction maps from images of a population of individual DNA molecules (clones) digested by restriction enzymes. The original algorithm was capable of producing highresolutio ..."
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Cited by 4 (4 self)
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) Thomas Anantharaman and Bud Mishra 1 Abstract In this paper, we extend an algorithmic approach to constructing ordered restriction maps from images of a population of individual DNA molecules (clones) digested by restriction enzymes. The original algorithm was capable of producing highresolution, highaccuracy maps rapidly and in a scalable manner given a certain class of data errors, including contamination, sizing errors, false and missing restriction sites and unknown orientation. Here we extend this set of errors to include possibly broken molecules where the amount of breakage is not known beforehand, which is necessary for handling larger clones. In an earlier paper [AMS97], we had shown that the problem of making maps from molecules with end fragments missing as the only source of error is NPcomplete. We also show how to handle multiple reliability levels in the input data when calling restriction sites. 1 Genomics and Optical Mapping Optical mapping [CAH+95, CJI+96, HRL...
A Uniform Framework for Ordered Restriction Map Problems
 York University
, 1997
"... Optical Mapping is an emerging technology for constructing ordered restriction maps of DNA molecules [1, 2, 3]. The underlying computational problems for this technology have been studied and several cost functions have been proposed in recent literature. Most of these propose combinatorial model ..."
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Cited by 4 (3 self)
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Optical Mapping is an emerging technology for constructing ordered restriction maps of DNA molecules [1, 2, 3]. The underlying computational problems for this technology have been studied and several cost functions have been proposed in recent literature. Most of these propose combinatorial models; one of them also presents a probabilistic approach. However, it is not a priori clear as to how these cost functions relate to one another and to the underlying problem. We present a uniform framework for the restriction map problems where each of these various models is a specific instance of the basic framework. We achieve this by identifying the following approaches to the ordered restriction map problem: (1) using data consensus or agreement, and, (2) optimizing a characteristic function of the data. Our framework also opens up the possibility of exploring other cost functions. An additional feature is that we not only integrate the combinatorial models but also analyze the pro...
Partitioning K Clones: Hardness Results and Practical Algorithms for the KPopulations Problem
 In Proc. RECOMB 98
, 1998
"... Given a set of m molecules, derived from K homologous clones, we wish to partition these molecules into K populations, each giving rise to distinct ordered restriction maps, thus providing simple means for studying biological variations. With the emergence of single molecule methods, such as optica ..."
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Cited by 3 (1 self)
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Given a set of m molecules, derived from K homologous clones, we wish to partition these molecules into K populations, each giving rise to distinct ordered restriction maps, thus providing simple means for studying biological variations. With the emergence of single molecule methods, such as optical mapping, that can create individual ordered restriction maps reliably and with high throughput, it becomes interesting to study the related algorithmic problems. In particular, we provide a complete computational complexity analysis of the "Kpopulations " problem as well as some simple polynomial heuristics, while exposing the relations among various error sources that the optical mapping approach may need to cope with. We believe that these results will be of interest to computational biologists in devising better algorithms, to biochemists in understanding the tradeoffs among the error sources and finally, to biologists in creating reliable protocols for population study. 1 Introductio...
Fast and cheap genome wide haplotype construction via optical mapping
 385– 396. Pacific Symposium on Biocomputing
, 2005
"... We describe an efficient algorithm to construct genome wide haplotype restriction maps of an individual by aligning single molecule DNA fragments collected with Optical Mapping technology. Using this algorithm and small amount of genomic material, we can construct the parental haplotypes for each di ..."
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Cited by 3 (2 self)
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We describe an efficient algorithm to construct genome wide haplotype restriction maps of an individual by aligning single molecule DNA fragments collected with Optical Mapping technology. Using this algorithm and small amount of genomic material, we can construct the parental haplotypes for each diploid chromosome for any individual. Since such haplotype maps reveal the polymorphisms due to single nucleotide differences (SNPs) and small insertions and deletions (RFLPs), they are useful in association studies, studies involving genomic instabilities in cancer, and genetics, and yet incur relatively low cost and provide high throughput. If the underlying problem is formulated as a combinatorial optimization problem, it can be shown to be NPcomplete (a special case of Kpopulation problem). But by effectively exploiting the structure of the underlying error processes and using a novel analog of the BaumWelch algorithm for HMM models, we devise a probabilistic algorithm with a time complexity that is linear in the number of markers for an ǫapproximate solution. The algorithms were tested by constructing the first genome wide haplotype restriction map of the microbe T. pseudoana, as well as constructing a haplotype restriction map of a 120 Mb region of Human chromosome 4. The frequency of false positives and false negatives was estimated using simulated data. The empirical results were found very promising. 1.
Inapproximability of FlipCut, ShiftCut and other problems from Optical Mapping
 York University
, 1997
"... Optical Mapping is an emerging technology for constructing ordered restriction maps of DNA molecules. The study of the complexity of the problems arising in Optical Mapping has generated considerable interest amongst computer science researchers [9], [10], [11], [12], [13]. In this paper we examine ..."
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Cited by 1 (1 self)
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Optical Mapping is an emerging technology for constructing ordered restriction maps of DNA molecules. The study of the complexity of the problems arising in Optical Mapping has generated considerable interest amongst computer science researchers [9], [10], [11], [12], [13]. In this paper we examine the complexity of these problems. Optical Mapping leads to various computational problems such as the Binary Flip Cut (BFC) problem [9, 10], the Weighted Flip Cut (WFC) problem [10] the Exclusive Binary Flip Cut (EBFC) problem [9, 10], the Binary Shift Cut (BSC) problem [12, 11], the Binary Partition Cut (BPC) [12] problem and others. The complexity and the hardness of the BFC problem [9], the WFC problem [10] were not known. Using the technique of gappreserving reduction (see [7, 8]) of the maxcut problem, we show that BFC and WFC problems are MAX SNPhard [6] and achieving an approximation ratio 1 \Gamma \Upsilon=7 for these problems is NPhard, where \Upsilon denotes the upper bound on ...