Programming pearls

Bentley, Jon Louis

doi:10.1145/358413.383461

Cited by 20 publications

(33 citation statements)

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“…A length cutoff L is given to avoid reporting extremely short optimal regions. Huang extended the well-known recurrence relation used by Bentley [6] for solving the maximum sum consecutive subsequence problem, and derived a linear-time algorithm for computing the optimal segments with lengths at least…”

Section: Locating Gc-rich Regionsmentioning

confidence: 99%

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Efficient Algorithms for Locating the Length-Constrained Heaviest Segments, with Applications to Biomolecular Sequence Analysis

Lin

Jiang

Chao

2002

Lecture Notes in Computer Science

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Abstract.We study two fundamental problems concerning the search for interesting regions in sequences: (i) given a sequence of real numbers of length n and an upper bound U , find a consecutive subsequence of length at most U with the maximum sum and (ii) given a sequence of real numbers of length n and a lower bound L, find a consecutive subsequence of length at least L with the maximum average. We present an O(n)-time algorithm for the first problem and an O(n log L)-time algorithm for the second. The algorithms have potential applications in several areas of biomolecular sequence analysis including locating GC-rich regions in a genomic DNA sequence, post-processing sequence alignments, annotating multiple sequence alignments, and computing length-constrained ungapped local alignment. Our preliminary tests on both simulated and real data demonstrate that the algorithms are very efficient and able to locate useful (such as GC-rich) regions.

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Section: Locating Gc-rich Regionsmentioning

confidence: 99%

“…tained [13] by extending the dynamically algorithm for the standard maximum sum consecutive subsequence problem in [6].…”

Section: Introductionmentioning

confidence: 99%

Efficient Algorithms for Locating the Length-Constrained Heaviest Segments, with Applications to Biomolecular Sequence Analysis

Lin

Jiang

Chao

2002

Lecture Notes in Computer Science

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“…Given a sequence of real numbers, the maximum subsequence problem finds the contiguous subsequence with the maximum sum [3]. A more general problem is the all maximal subsequences problem [8] which finds a list of all non-overlapping contiguous subsequences with maximal sum.…”

Section: Introductionmentioning

confidence: 99%

A BSP/CGM Algorithm for Finding All Maximal Contiguous Subsequences of a Sequence of Numbers

Alves

Cáceres

Song

2006

Euro-Par 2006 Parallel Processing

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Abstract. Given a sequence A of real numbers, we wish to find a list of all non-overlapping contiguous subsequences of A that are maximal. A maximal subsequence M of A has the property that no proper subsequence of M has a greater sum of values. Furthermore, M may not be contained properly within any subsequence of A with this property. This problem can be solved sequentially in linear time. We present a BSP/CGM algorithm that uses p processors and takes O(|A|/p) time and O(|A|/p) space per processor. The algorithm uses a constant number of communication rounds of size at most O(|A|/p). Thus the algorithm achieves linear speed-up and is highly scalable.

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“…1 For brevity, we will refer to these as an L constraint and/or U constraint. In addition, the heaviest segment problem with no constraints on segment length is discussed by Bentley [5]. (This version of the problem was motivated by image processing tasks.)…”

Section: Introductionmentioning

confidence: 99%

“…The first result was an unpublished result of Kadane [5] for the unconstrained heaviest segment problem. This solution uses O(n) time and constant space (be-yond the space used to represent the input) 2 .…”

Section: Introductionmentioning

confidence: 99%

Fast and Space-Efficient Location of Heavy or Dense Segments in Run-Length Encoded Sequences

Greenberg

2003

Lecture Notes in Computer Science

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Abstract. This paper considers several variations of an optimization problem with potential applications in such areas as biomolecular sequence analysis and image processing. Given a sequence of items, each with a weight and a length, the goal is to find a subsequence of consecutive items of optimal value, where value is either total weight or total weight divided by total length. There may also be a specified lower and/or upper bound on the acceptable length of subsequences. This paper shows that all the variations of the problem are solvable in linear time and space even with non-uniform item lengths and divisible items, implying that run-length encoded sequences can be handled in time and space linear in the number of runs. Furthermore, some problem variations can be solved in constant space. Also, these time and space bounds suffice for certain problem variations in which we call for reporting of many "good" subsequences.

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Programming pearls

Cited by 20 publications

References 0 publications

Efficient Algorithms for Locating the Length-Constrained Heaviest Segments, with Applications to Biomolecular Sequence Analysis

Efficient Algorithms for Locating the Length-Constrained Heaviest Segments, with Applications to Biomolecular Sequence Analysis

A BSP/CGM Algorithm for Finding All Maximal Contiguous Subsequences of a Sequence of Numbers

Fast and Space-Efficient Location of Heavy or Dense Segments in Run-Length Encoded Sequences

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