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.

Dynamic Programming Approach for Online Freeway Flow Propagation Adjustment

2002 ◽  
Vol 1802 (1) ◽  
pp. 263-270 ◽  
Author(s):  
Xuesong Zhou ◽  
Hani S. Mahmassani
Keyword(s):  
Dynamic Programming ◽  
Control Method ◽  
Dynamic Programming Algorithm ◽  
Superior Performance ◽  
Programming Algorithm ◽  
Programming Approach ◽  
Base Case ◽  
Solution Quality ◽  
Flow Propagation ◽  
The Impact

An optimization framework for online flow propagation adjustment in a freeway context was proposed. Instead of performing local adjustment for individual links separately, the proposed framework considers the interconnectivity of links in a traffic network. In particular, dynamic behavior in the mesoscopic simulation is approximated by the finite-difference method at a macroscopic level. The proposed model seeks to minimize the deviation between simulated density and anticipated density. By taking advantage of the serial structure of a freeway, an efficient dynamic programming algorithm has been developed and tested. The experiment results compared with analytic results as the base case showed the superior performance of dynamic programming methods over the classical proportion control method. The effect of varying update intervals was also examined. The simulation results suggest that a greedy method considering the impact of inconsistency propagation achieves the best trade-off in terms of computation effort and solution quality.

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 Optimal Common Contract with Heterogeneous Agents

2020 ◽  
Vol 34 (05) ◽  
pp. 7309-7316
Author(s):  
Shenke Xiao ◽  
Zihe Wang ◽  
Mengjing Chen ◽  
Pingzhong Tang ◽  
Xiwang Yang
Keyword(s):  
Dynamic Programming ◽  
Heterogeneous Agents ◽  
Dynamic Programming Algorithm ◽  
Incentive Contracts ◽  
Approximate Algorithm ◽  
Programming Algorithm ◽  
Optimal Contract ◽  
Difference Property ◽  
Principal Agent Problem ◽  
Np Complete

We consider the principal-agent problem with heterogeneous agents. Previous works assume that the principal signs independent incentive contracts with every agent to make them invest more efforts on the tasks. However, in many circumstances, these contracts need to be identical for the sake of fairness. We investigate the optimal common contract problem. To our knowledge, this is the first attempt to consider this natural and important generalization. We first show this problem is NP-complete. Then we provide a dynamic programming algorithm to compute the optimal contract in O(n2m) time, where n,m are the number of agents and actions, under the assumption that the agents' cost functions obey increasing difference property. At last, we generalize the setting such that each agent can choose to directly produce a reward in [0,1]. We provide an O(log n)-approximate algorithm for this generalization.

scholarly journals Are all global alignment algorithms and implementations correct?

2015 ◽  
Author(s):  
Tomáš Flouri ◽  
Kassian Kobert ◽  
Torbjørn Rognes ◽  
Alexandros Stamatakis
Keyword(s):  
Dynamic Programming ◽  
Phylogenetic Analyses ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Global Alignment ◽  
Sequence Alignments ◽  
Optimal Sequence ◽  
Divergence Time Estimates ◽  
Alignment Algorithms ◽  
The Impact

While implementing the algorithm, we discovered two mathematical mistakes in Gotoh's paper that induce sub-optimal sequence alignments. First, there are minor indexing mistakes in the dynamic programming algorithm which become apparent immediately when implementing the procedure. Hence, we report on these for the sake of completeness. Second, there is a more profound problem with the dynamic programming matrix initialization. This initialization issue can easily be missed and find its way into actual implementations. This error is also present in standard text books. Namely, the widely used books by Gusfield and Waterman. To obtain an initial estimate of the extent to which this error has been propagated, we scrutinized freely available undergraduate lecture slides. We found that 8 out of 31 lecture slides contained the mistake, while 16 out of 31 simply omit parts of the initialization, thus giving an incomplete description of the algorithm. Finally, by inspecting ten source codes and running respective tests, we found that five implementations were incorrect. Note that, not all bugs we identified are due to the mistake in Gotoh's paper. Three implementations rely on additional constraints that limit generality. Thus, only two out of ten yield correct results. We show that the error introduced by Gotoh is straightforward to resolve and provide a correct open-source reference implementation. We do believe though, that raising the awareness about these errors is critical, since the impact of incorrect pairwise sequence alignments that typically represent one of the very first stages in any bioinformatics data analysis pipeline can have a detrimental impact on downstream analyses such as multiple sequence alignment, orthology assignment, phylogenetic analyses, divergence time estimates, etc.

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.

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.

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