ON COMPARING TWO STRUCTURED RNA MULTIPLE ALIGNMENTS

2010 ◽  
Vol 08 (06) ◽  
pp. 967-980 ◽  
Author(s):  
VANDANABEN PATEL ◽  
JASON T. L. WANG ◽  
SHEFALI SETIA ◽  
ANURAG VERMA ◽  
CHARLES D. WARDEN ◽  
...  
Keyword(s):  
Dynamic Programming Algorithm ◽  
Web Server ◽  
Pairwise Alignment ◽  
Programming Algorithm ◽  
Multiple Sequence ◽  
Consensus Secondary Structure ◽  
Time Dynamic ◽  
Multiple Alignments ◽  
Alignment Process ◽  
Alignment Result

We present a method, called BlockMatch, for aligning two blocks, where a block is an RNA multiple sequence alignment with the consensus secondary structure of the alignment in Stockholm format. The method employs a quadratic-time dynamic programming algorithm for aligning columns and column pairs of the multiple alignments in the blocks. Unlike many other tools that can perform pairwise alignment of either single sequences or structures only, BlockMatch takes into account the characteristics of all the sequences in the blocks along with their consensus structures during the alignment process, thus being able to achieve a high-quality alignment result. We apply BlockMatch to phylogeny reconstruction on a set of 5S rRNA sequences taken from fifteen bacteria species. Experimental results showed that the phylogenetic tree generated by our method is more accurate than the tree constructed based on the widely used ClustalW tool. The BlockMatch algorithm is implemented into a web server, accessible at . A jar file of the program is also available for download from the web server.

Single Item Lot Sizing Models with Bounded Inventory and Remanufacturing

2010 ◽  
Vol 102-104 ◽  
pp. 791-795
Author(s):  
Neng Min Wang ◽  
Zheng Wen He ◽  
Qiu Shuang Zhang ◽  
Lin Yan Sun
Keyword(s):  
Lot Sizing ◽  
Dynamic Programming Algorithm ◽  
Production Capacity ◽  
Planning Horizon ◽  
Programming Algorithm ◽  
Single Item ◽  
Time Dynamic ◽  
Lot Sizing Problem ◽  
Dynamic Lot Sizing ◽  
Finite Planning Horizon

Dynamic lot sizing problem for systems with bounded inventory and remanufacturing was addressed. The demand and return amounts are deterministic over the finite planning horizon. Demands can be satisfied by manufactured new items, but also by remanufactured returned items. In production planning, there can be situations where the ability to meet customer demands is constrained by inventory capacity rather than production capacity. Two different limited inventory capacities are considered; there is either bounded serviceables inventory or bounded returns inventory. For the two inventory case, we present exact, polynomial time dynamic programming algorithm based on the idea of Teunter R, et al. (2006).

OPTIMAL PAIRWISE ALIGNMENT OF FIXED PROTEIN STRUCTURES IN SUBQUADRATIC TIME

2011 ◽  
Vol 09 (03) ◽  
pp. 367-382 ◽  
Author(s):  
ALEKSANDAR POLEKSIC
Keyword(s):  
Protein Structure ◽  
Structural Alignment ◽  
Protein Structures ◽  
Dynamic Programming Algorithm ◽  
Pairwise Alignment ◽  
Structure Alignment ◽  
Programming Algorithm ◽  
Protein Structure Alignment ◽  
Running Time ◽  
Speed Accuracy

The problem of finding an optimal structural alignment for a pair of superimposed proteins is often amenable to the Smith–Waterman dynamic programming algorithm, which runs in time proportional to the product of lengths of the sequences being aligned. While the quadratic running time is acceptable for computing a single alignment of two fixed protein structures, the time complexity becomes a bottleneck when running the Smith–Waterman routine multiple times in order to find a globally optimal superposition and alignment of the input proteins. We present a subquadratic running time algorithm capable of computing an alignment that optimizes one of the most widely used measures of protein structure similarity, defined as the number of pairs of residues in two proteins that can be superimposed under a predefined distance cutoff. The algorithm presented in this article can be used to significantly improve the speed–accuracy tradeoff in a number of popular protein structure alignment methods.

scholarly journals On the exact separation of cover inequalities of maximum-depth

2021 ◽  
Author(s):  
Daniele Catanzaro ◽  
Stefano Coniglio ◽  
Fabio Furini
Keyword(s):  
Dynamic Programming ◽  
Knapsack Problem ◽  
Dynamic Programming Algorithm ◽  
Maximum Depth ◽  
Knapsack Problems ◽  
Programming Algorithm ◽  
Separation Problem ◽  
Time Dynamic ◽  
Cover Inequalities ◽  
Exact Separation

AbstractWe investigate the problem of separating cover inequalities of maximum-depth exactly. We propose a pseudopolynomial-time dynamic-programming algorithm for its solution, thanks to which we show that this problem is weakly $${\mathcal {N}}{\mathcal {P}}$$ N P -hard (similarly to the problem of separating cover inequalities of maximum violation). We carry out extensive computational experiments on instances of the knapsack and the multi-dimensional knapsack problems with and without conflict constraints. The results show that, with a cutting-plane generation method based on the maximum-depth criterion, we can optimize over the cover-inequality closure by generating a number of cuts smaller than when adopting the standard maximum-violation criterion. We also introduce the Point-to-Hyperplane Distance Knapsack Problem (PHD-KP), a problem closely related to the separation problem for maximum-depth cover inequalities, and show how the proposed dynamic programming algorithm can be adapted for effectively solving the PHD-KP as well.

scholarly journals Dynamic Programming Algorithms Applied to Musical Counterpoint in Process Composition: An Example Using Henri Pousseur’s Scambi

2020 ◽  
Author(s):  
Louis J. Cochrane ◽  
Derek Gatherer
Keyword(s):  
Dynamic Programming ◽  
Electronic Music ◽  
Dynamic Programming Algorithm ◽  
Pairwise Alignment ◽  
Distance Matrix ◽  
Programming Algorithm ◽  
Biological Sequence ◽  
Dynamic Programming Matrix ◽  
Process Composition ◽  
Programming Algorithms

The Needleman-Wunsch process is a classic tool in bioinformatics, being a dynamic programming algorithm that performs a pairwise alignment of two input biological sequences, either protein or nucleic acid. A distance matrix between the tokens used in the sequences is also required as input. The distance matrix is used to generate a positional pairwise similarity matrix between the input sequences, which is in turn used to generate a dynamic programming matrix. The best path through the dynamic programming matrix is navigated using a traceback procedure that maximises similarity, inserting gaps as necessary. Needleman-Wunsch can align both nucleic acids or proteins, which use alphabets of size 4 and 20 tokens respectively. It can also be applied to any other kind of sequence where distance matrices can be specified. Here, we apply it to chains of Pousseur’s Scambi electronic music fragments, of which there are 32, and which Pousseur categorised by their sonic properties, thus permitting the consecutive construction of distance, similarity and dynamic programming matrices. Traceback through the dynamic programming matrix thus produces contrapuntal duet compositions in which two Scambi chains are played in the maximally euphonious manner, providing also an illustration of the principles of biological sequence alignment in sound.

scholarly journals Folding Polyominoes into (Poly)Cubes

2018 ◽  
Vol 28 (03) ◽  
pp. 197-226 ◽  
Author(s):  
Oswin Aichholzer ◽  
Michael Biro ◽  
Erik D. Demaine ◽  
Martin L. Demaine ◽  
David Eppstein ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Linear Time ◽  
Dynamic Programming Algorithm ◽  
Unit Cube ◽  
Programming Algorithm ◽  
Regular Tetrahedron ◽  
Time Dynamic ◽  
Constant Size ◽  
Inclusion Relations

We study the problem of folding a polyomino [Formula: see text] into a polycube [Formula: see text], allowing faces of [Formula: see text] to be covered multiple times. First, we define a variety of folding models according to whether the folds (a) must be along grid lines of [Formula: see text] or can divide squares in half (diagonally and/or orthogonally), (b) must be mountain or can be both mountain and valley, (c) can remain flat (forming an angle of [Formula: see text]), and (d) must lie on just the polycube surface or can have interior faces as well. Second, we give all the inclusion relations among all models that fold on the grid lines of [Formula: see text]. Third, we characterize all polyominoes that can fold into a unit cube, in some models. Fourth, we give a linear-time dynamic programming algorithm to fold a tree-shaped polyomino into a constant-size polycube, in some models. Finally, we consider the triangular version of the problem, characterizing which polyiamonds fold into a regular tetrahedron.

REACHABILITY ANALYSIS FOR UNCERTAIN SSPs

2007 ◽  
Vol 16 (04) ◽  
pp. 725-749
Author(s):  
OLIVIER BUFFET
Keyword(s):  
Transition Probability ◽  
Dynamic Programming Algorithm ◽  
Complex Case ◽  
Programming Algorithm ◽  
Time Dynamic ◽  
Goal State ◽  
Stochastic Shortest Path ◽  
Shortest Path Problems ◽  
Complete State ◽  
Stochastic Shortest Path Problems

Stochastic Shortest Path problems (SSPs) can be efficiently dealt with by the Real-Time Dynamic Programming algorithm (RTDP). Yet, RTDP requires that a goal state is always reachable. This article presents an algorithm checking for goal reachability, especially in the complex case of an uncertain SSP where only a possible interval is known for each transition probability. This gives an analysis method for determining if SSP algorithms such as RTDP are applicable, even if the exact model is not known. As this is a time-consuming algorithm, we also present a simple process that often speeds it up dramatically. Yet, the main improvement still needed is to turn to a symbolic analysis in order to avoid a complete state-space enumeration.

scholarly journals LinearFold: linear-time approximate RNA folding by 5'-to-3' dynamic programming and beam search

2019 ◽  
Vol 35 (14) ◽  
pp. i295-i304 ◽  
Author(s):  
Liang Huang ◽  
He Zhang ◽  
Dezhong Deng ◽  
Kai Zhao ◽  
Kaibo Liu ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Computational Linguistics ◽  
Rna Folding ◽  
Linear Time ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Supplementary Information ◽  
Programming Algorithm ◽  
Time Dynamic ◽  
Approximate Search

Abstract Motivation Predicting the secondary structure of an ribonucleic acid (RNA) sequence is useful in many applications. Existing algorithms [based on dynamic programming] suffer from a major limitation: their runtimes scale cubically with the RNA length, and this slowness limits their use in genome-wide applications. Results We present a novel alternative O(n3)-time dynamic programming algorithm for RNA folding that is amenable to heuristics that make it run in O(n) time and O(n) space, while producing a high-quality approximation to the optimal solution. Inspired by incremental parsing for context-free grammars in computational linguistics, our alternative dynamic programming algorithm scans the sequence in a left-to-right (5′-to-3′) direction rather than in a bottom-up fashion, which allows us to employ the effective beam pruning heuristic. Our work, though inexact, is the first RNA folding algorithm to achieve linear runtime (and linear space) without imposing constraints on the output structure. Surprisingly, our approximate search results in even higher overall accuracy on a diverse database of sequences with known structures. More interestingly, it leads to significantly more accurate predictions on the longest sequence families in that database (16S and 23S Ribosomal RNAs), as well as improved accuracies for long-range base pairs (500+ nucleotides apart), both of which are well known to be challenging for the current models. Availability and implementation Our source code is available at https://github.com/LinearFold/LinearFold, and our webserver is at http://linearfold.org (sequence limit: 100 000nt). Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals A Polynomial-Time Dynamic Programming Algorithm for Phrase-Based Decoding with a Fixed Distortion Limit

2017 ◽  
Vol 5 ◽  
pp. 59-71
Author(s):  
Yin-Wen Chang ◽  
Michael Collins
Keyword(s):  
Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Sentence Length ◽  
Target Language ◽  
Programming Algorithm ◽  
Time Dynamic ◽  
Np Complete ◽  
New Perspective ◽  
The Traveling Salesman Problem ◽  
The Impact

Decoding of phrase-based translation models in the general case is known to be NP-complete, by a reduction from the traveling salesman problem (Knight, 1999). In practice, phrase-based systems often impose a hard distortion limit that limits the movement of phrases during translation. However, the impact on complexity after imposing such a constraint is not well studied. In this paper, we describe a dynamic programming algorithm for phrase-based decoding with a fixed distortion limit. The runtime of the algorithm is O( nd! lh d+1) where n is the sentence length, d is the distortion limit, l is a bound on the number of phrases starting at any position in the sentence, and h is related to the maximum number of target language translations for any source word. The algorithm makes use of a novel representation that gives a new perspective on decoding of phrase-based models.

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