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18
Perspectives of Monge Properties in Optimization
, 1995
"... An m × n matrix C is called Monge matrix if c ij + c rs c is + c rj for all 1 i ! r m, 1 j ! s n. In this paper we present a survey on Monge matrices and related Monge properties and their role in combinatorial optimization. Specifically, we deal with the following three main topics: (i) funda ..."
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Cited by 53 (3 self)
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An m × n matrix C is called Monge matrix if c ij + c rs c is + c rj for all 1 i ! r m, 1 j ! s n. In this paper we present a survey on Monge matrices and related Monge properties and their role in combinatorial optimization. Specifically, we deal with the following three main topics: (i) fundamental combinatorial properties of Monge structures, (ii) applications of Monge properties to optimization problems and (iii) recognition of Monge properties.
Computing similarity between rna strings
, 1996
"... Ribonucleic acid (RNA) strings are strings over the fourletter alphabet {A, C, G, U} with a secondary structure of basepairing between A U and C G pairs in the string 1. Edges are drawn between two bases that are paired in the secondary structure and these edges have traditionally been assumed t ..."
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Cited by 36 (4 self)
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Ribonucleic acid (RNA) strings are strings over the fourletter alphabet {A, C, G, U} with a secondary structure of basepairing between A U and C G pairs in the string 1. Edges are drawn between two bases that are paired in the secondary structure and these edges have traditionally been assumed to be noncrossing. The noncrossing basepairing naturally leads to a treelike representation of the secondary structure of RNA strings. In this paper, we address several notions of similarity between two RNA strings that take into account both the primary sequence and secondary basepalring structure of the strings. We present efficient algorithms for exact matching and approximate matching between two RNA strings. We define a notion of alignment between two RNA strings and devise algorithms based on dynamic programming. We then present a method for optimally aligning a given RNA string with unknown secondary structure to one with known sequence and structure, thus attacking the structure prediction problem in the case when the structure of a closely related sequence is known. The techniques employed to prove our results include reductions to wellknown string matching problems allowing wild cards and ranges, and speeding up dynamic programming by using the tree structures implicit in the secondary structure of RNA strings.
Linear and O(n log n) Time MinimumCost Matching Algorithms for Quasiconvex Tours (Extended Abstract)
"... Samuel R. Buss # Peter N. Yianilos + Abstract Let G be a complete, weighted, undirected, bipartite graph with n red nodes, n # blue nodes, and symmetric cost function c(x, y) . A maximum matching for G consists of min{n, n # edges from distinct red nodes to distinct blue nodes. Our objective is ..."
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Cited by 17 (3 self)
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Samuel R. Buss # Peter N. Yianilos + Abstract Let G be a complete, weighted, undirected, bipartite graph with n red nodes, n # blue nodes, and symmetric cost function c(x, y) . A maximum matching for G consists of min{n, n # edges from distinct red nodes to distinct blue nodes. Our objective is to find a minimumcost maximum matching, i.e. one for which the sum of the edge costs has minimal value. This is the weighted bipartite matching problem; or as it is sometimes called, the assignment problem.
A Study of Accessible Motifs and RNA Folding Complexity
"... Abstract. mRNA molecules are folded in the cells and therefore many of their substrings may actually be inaccessible to protein and microRNA binding. The need to apply an accessability criterion to the task of genomewide mRNA motif discovery raises the challenge of overcoming the core O(n 3) factor ..."
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Cited by 14 (1 self)
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Abstract. mRNA molecules are folded in the cells and therefore many of their substrings may actually be inaccessible to protein and microRNA binding. The need to apply an accessability criterion to the task of genomewide mRNA motif discovery raises the challenge of overcoming the core O(n 3) factor imposed by the time complexity of the currently best known algorithms for RNA secondary structure prediction [24, 25, 43]. We speed up the dynamic programming algorithms that are standard for RNA folding prediction. Our new approach significantly reduces the computations without sacrificing the optimality of the results, yielding an expected time complexity of O(n 2 ψ(n)), whereψ(n) is shown to be constant on average under standard polymer folding models. Benchmark analysis confirms that in practice the runtime ratio between the previous approach and the new algorithm indeed grows linearly with increasing sequence size. The fast new RNA folding algorithm is utilized for genomewide discovery of accessible cisregulatory motifs in data sets of ribosomal densities and decay rates of S. cerevisiae genes and to the mining of exposed binding sites of tissuespecific microRNAs in A. Thaliana. Further details, including additional figures and proofs to all lemmas, can be found at:
Multiple sequence alignment with arbitrary gap costs: Computing an optimal solution using polyhedral combinatorics
, 2002
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Constructing Huffman Trees in Parallel
 SIAM Journal on Computing
, 1995
"... We present a parallel algorithm for the Huffman Coding problem. We reduce the Huffman Coding problem to the Concave Least Weight Subsequence problem and give a parallel algorithm that solves the latter problem in O( p n log n) time with n processors on a CREW PRAM. This leads to the first sublinea ..."
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Cited by 9 (0 self)
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We present a parallel algorithm for the Huffman Coding problem. We reduce the Huffman Coding problem to the Concave Least Weight Subsequence problem and give a parallel algorithm that solves the latter problem in O( p n log n) time with n processors on a CREW PRAM. This leads to the first sublinear time o(n 2 )total work parallel algorithm for Huffman Coding. This reduction of the Huffman Coding problem to the Concave Least Weight Subsequence problem also yields an alternative O(n log n)time (or linear time  for a sorted input sequence) algorithm for Huffman Coding. This research was supported by NSF grant CCR9112067. y Part of this work was done while the author was visiting the University of California, Riverside. 1 Introduction Throughout this paper, a tree is a regular binary tree (i.e. a binary tree in which each internal node has two children). The level of a node in a tree is its distance from the root. The problem of constructing a Huffman tree is, given a seque...
A highthroughput approach for associating microRNAs with their activity conditions
 J. Comput. Biol
, 2006
"... Abstract Plant microRNAs (miRNAs) are short RNA sequences that bind to target mRNAs and change theirexpression levels by influencing their stabilities and marking them for cleavage. We present a high throughput approach for associating between microRNAs and conditions in which they act, using novels ..."
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Cited by 5 (1 self)
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Abstract Plant microRNAs (miRNAs) are short RNA sequences that bind to target mRNAs and change theirexpression levels by influencing their stabilities and marking them for cleavage. We present a high throughput approach for associating between microRNAs and conditions in which they act, using novelstatistical and algorithmic measures. Our new prototype tool, miRNAXpress, computes a (binary) matrix T denoting the potential targets of microRNAs. Then, using T and an additional predefined matrix X indicating expression of genes under various conditions, it produces a new matrix that predicts associations between microRNAs and the conditions in which they act.The computational intensive part of miRNAXpress is the calculation of T. We provide a hybridizationsearch algorithm which given a query microRNA, a text mRNA, and a predefined energy cutoff threshold, finds and reports all targets (putative binding sites) of the query in the text with binding energy belowthe predefined threshold. In order to speed it up, we utilize the sparsity of the search space without sacrificing the optimality of the results. Consequently, the time complexity of the search algorithm isalmost linear in the size of a sparse set of locations where basepairs are stacked at a height of three or more.We employed our tool to conduct a study, using the plant Arabidopsis thaliana as our model organism. By applying miRNAXpress to 98 microRNAs and 380 conditions, some biologically interesting andstatistically strong relations were discovered.
The algebraic Monge property and path problems
 Discrete Applied Mathematics
"... We give algorithmic results for combinatorial problems with cost arrays possessing certain algebraic Monge properties. We extend Mongearray results for two shortest path problems to a general algebraic setting, with values in an ordered commutative semigroup, if the semigroup operator is strictly c ..."
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Cited by 2 (0 self)
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We give algorithmic results for combinatorial problems with cost arrays possessing certain algebraic Monge properties. We extend Mongearray results for two shortest path problems to a general algebraic setting, with values in an ordered commutative semigroup, if the semigroup operator is strictly compatible with the order relation. We show how our algorithms can be modified to solve bottleneck shortest path problems, even though strict compatibility does not hold in that case. For example, we give a linear time algorithm for the unrestricted shortest path bottleneck problem on n nodes, also O(kn) and O(n 3/2 log 5/2 n) time algorithms for the kshortest path bottleneck problem.
Computational Biology
, 2000
"... During four years of arduous service, a Ph. D. student is expected to familiarise himself with his field of research, and, hopefully, contribute to this field. This is reflected by the division of this dissertation into two parts. Part I is a (partial) overview of the field of computational biology ..."
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Cited by 1 (0 self)
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During four years of arduous service, a Ph. D. student is expected to familiarise himself with his field of research, and, hopefully, contribute to this field. This is reflected by the division of this dissertation into two parts. Part I is a (partial) overview of the field of computational biology as I conceive it, an overview that is aimed at presenting the context for my contributions to the field of computational biology. These contributions are presented in part II as five independent articles
Efficient Algorithms for Sequence Analysis
 Proc. Second Workshop on Sequences: Combinatorics, Compression. Securiry
, 1991
"... : We consider new algorithms for the solution of many dynamic programming recurrences for sequence comparison and for RNA secondary structure prediction. The techniques upon which the algorithms are based e#ectively exploit the physical constraints of the problem to derive more e#cient methods f ..."
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Cited by 1 (0 self)
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: We consider new algorithms for the solution of many dynamic programming recurrences for sequence comparison and for RNA secondary structure prediction. The techniques upon which the algorithms are based e#ectively exploit the physical constraints of the problem to derive more e#cient methods for sequence analysis. 1. INTRODUCTION In this paper we consider algorithms for two problems in sequence analysis. The first problem is sequence alignment, and the second is the prediction of RNA structure. Although the two problems seem quite di#erent from each other, their solutions share a common structure, which can be expressed as a system of dynamic programming recurrence equations. These equations also can be applied to other problems, including text formatting and data storage optimization. We use a number of well motivated assumptions about the problems in order to provide e#cient algorithms. The primary assumption is that of concavity or convexity. The recurrence relations for bo...