Results 1  10
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14
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
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Cited by 289 (2 self)
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We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m + n log n +kn). We describe applications to dynamic programming problems including the knapsack problem, sequence alignment, maximum inscribed polygons, and genealogical relationship discovery. 1 Introduction We consider a longstudied generalization of the shortest path problem, in which not one but several short paths must be produced. The k shortest paths problem is to list the k paths connecting a given sourcedestination pair in the digraph with minimum total length. Our techniques also apply to the problem of listing all paths shorter than some given threshhold length. In the version of these problems studi...
Optimal alignments in linear space
 CABIOS
, 1988
"... Space, not time, is often the limiting factor when computing optimal sequence alignments, and a number of recent papers in the biology literature have proposed spacesaving strategies. However, a 1975 computer science paper by Hirschberg presented a method that is superior to the newer proposals, bo ..."
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Cited by 181 (3 self)
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Space, not time, is often the limiting factor when computing optimal sequence alignments, and a number of recent papers in the biology literature have proposed spacesaving strategies. However, a 1975 computer science paper by Hirschberg presented a method that is superior to the newer proposals, both in theory and in practice. The goal of this note is to give Hirschberg’s idea the visibility it deserves by developing a linearspace version of Gotoh’s algorithm, which accommodates affine gap penalties. A portable Csoftware package implementing this algorithm is available on the BIONET free of charge.
Predicting a set of minimal free energy RNA secondary structures common to two sequences
 Bioinformatics
, 2005
"... Function derives from structure; therefore there is need of methods for predicting functional RNA structures. Results: The Dynalign algorithm, which predicts the lowest free energy secondary structure common to two unaligned RNA sequences, is extended to the prediction of a set of low energy structu ..."
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Cited by 32 (4 self)
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Function derives from structure; therefore there is need of methods for predicting functional RNA structures. Results: The Dynalign algorithm, which predicts the lowest free energy secondary structure common to two unaligned RNA sequences, is extended to the prediction of a set of low energy structures. Dot plots can be drawn to show all base pairs in structures within an energy increment. Dynalign predicts more welldefined structures than structure prediction using a single sequence; in 5S rRNA sequences, the average number of base pairs in structures with energy within 20 % of the lowest energy structure is 317 using Dynalign, but 569 using a single sequence. Structure prediction with Dynalign can also be constrained according to experiment or comparative analysis. The accuracy, measured as sensitivity and positive predictive value, of Dynalign is greater than predictions with a single sequence. Availability: Dynalign can be downloaded at
A dynamic programming algorithm to find all solutions . . .
, 1985
"... Just after he introduced dynamic programming, Richard Bellman with R. Kalaba in 1960 gave a method for finding Kth best policies. Their method has been modified since then, but it is still not practical for many problems. This paper describes a new technique which modifies the usual backtracking pro ..."
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Cited by 29 (0 self)
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Just after he introduced dynamic programming, Richard Bellman with R. Kalaba in 1960 gave a method for finding Kth best policies. Their method has been modified since then, but it is still not practical for many problems. This paper describes a new technique which modifies the usual backtracking procedure and lists all nearoptimal policies. This practical algorithm is very much in the spirit of the original formulation of dynamic programming. An application to matching biological sequences is given.
NearOptimal Sequence Alignment
 Curr. Opin. Struct. Biol
, 1996
"... Introduction Aligning two short, similiar protein sequences by eye is an easy task. Teaching a machine the same skill turns out to be astonishingly difficult. Starting with the famous paper by Needleman and Wunsch [1] people have used dynamic programming algorithms to maximize the score associated ..."
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Cited by 16 (0 self)
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Introduction Aligning two short, similiar protein sequences by eye is an easy task. Teaching a machine the same skill turns out to be astonishingly difficult. Starting with the famous paper by Needleman and Wunsch [1] people have used dynamic programming algorithms to maximize the score associated with an alignment. While this algorithm is sometimes perceived as complicated the definition of an optimal sequence alignment is not. It is, in fact, simple. For proteins, pairs of residues are attributed a similarity score. With the aid of gaps (modeling insertions and deletions) the sum of these scores has to be maximized while the number and length of the gaps has to remain within biologically reasonable limits. This is achieved by subtracting penalties for gaps from the score for the matches. In a sense, it is astonishing how much biological information can be obtained using such a simple approach. A high alignment score between two proteins usually implies that sequences are homo
On Suboptimal Alignments of Biological Sequences
 Proc. 4th Symp. on Combinatorial Pattern Matching
, 1993
"... . It is widely accepted that the optimal alignmentbetween a pair of proteins or nucleic acid sequences that minimizes the edit distance may not necessarily re#ect the correct biological alignment. Alignments of proteins based on their structures or of DNA sequences based on evolutionary changes ..."
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Cited by 10 (0 self)
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. It is widely accepted that the optimal alignmentbetween a pair of proteins or nucleic acid sequences that minimizes the edit distance may not necessarily re#ect the correct biological alignment. Alignments of proteins based on their structures or of DNA sequences based on evolutionary changes are often di#erent from alignments that minimize edit distance. However, in many cases #e.g. when the sequences are close#, the edit distance alignment is a good approximation to the biological one. Since, for most sequences, the true alignment is unknown, a method that either assesses the signi#cance of the optimal alignment, or that provides few #close" alternatives to the optimal one, is of great importance. A suboptimal alignment is an alignment whose score lies within the neighborhood of the optimal score. Enumeration of suboptimal alignments #Wa83, WaBy# is not very practical since there are many such alignments. Other approaches #Zuk, Vi, ViAr# that use only partial informat...
Parametric Sequence Alignment with Constraints
 Constraints
"... Techniques for detecting similarities between biological sequences such as proteins and DNA are used as a fundamental tool by biologists to investigate the relationships between such sequences. Most of the similarity techniques are based on notions of string edit sequence which involve sequence alig ..."
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Cited by 2 (0 self)
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Techniques for detecting similarities between biological sequences such as proteins and DNA are used as a fundamental tool by biologists to investigate the relationships between such sequences. Most of the similarity techniques are based on notions of string edit sequence which involve sequence alignment using substitutions and deletions based on some cost measure. In this paper, we investigate algorithms which generalize the basic dynamic programming string edit distance algorithm to allow queries where the weight matrix of string edit costs is not fixed. Instead the costs can be nonground and the cost weights can also be constrained. A naive algorithm which uses inequalities to represent the alignment score is described and then an improved algorithm which greatly reduces the number of inequalities needed is developed. 1
The Match Game: New Stratigraphic Correlation Algorithms
 Math. Geol
, 1987
"... this paper accounts for such anomalies, respectively, though the ability to include single and multiple gaps in the correlations, through the ability to match a stratigraphic unit from one section with several adjacents units in the second section, and through the ability to compare both minimum dis ..."
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Cited by 2 (1 self)
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this paper accounts for such anomalies, respectively, though the ability to include single and multiple gaps in the correlations, through the ability to match a stratigraphic unit from one section with several adjacents units in the second section, and through the ability to compare both minimum distance and maximum similarity within a single correlation. Furthermore, based on one's knowledge of various depositional environments, different weighting schemes may be applied to account for chemical and physical variations occurring in the strata under study
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...