D-FLAT: Declarative problem solving using tree decompositions and answer-set programming

AbstractIn this work, we propose Answer-Set Programming (ASP) as a tool for rapid prototyping of dynamic programming algorithms based on tree decompositions. In fact, many such algorithms have been designed, but only a few of them found their way into implementation. The main obstacle is the lack of easy-to-use systems which (i) take care of building a tree decomposition and (ii) provide an interface for declarative specifications of dynamic programming algorithms. In this paper, we present D-FLAT, a novel tool that relieves the user of having to handle all the technical details concerned with parsing, tree decomposition, the handling of data structures, etc. Instead, it is only the dynamic programming algorithm itself which has to be specified in the ASP language. D-FLAT employs an ASP solver in order to compute the local solutions in the dynamic programming algorithm. In the paper, we give a few examples illustrating the use of D-FLAT and describe the main features of the system. Moreover, we report experiments which show that ASP-based D-FLAT encodings for some problems outperform monolithic ASP encodings on instances of small treewidth.

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Dynamic Programming Algorithms for Computing Optimal Knockout Tournaments

Mathematics ◽

10.3390/math9192480 ◽

2021 ◽

Vol 9 (19) ◽

pp. 2480

Author(s):

Amelia Bădică ◽

Costin Bădică ◽

Ion Buligiu ◽

Liviu Ion Ciora ◽

Doina Logofătu

Keyword(s):

Dynamic Programming ◽

Complexity Analysis ◽

Dynamic Programming Algorithm ◽

Experimental Results ◽

Programming Algorithm ◽

Programming Approach ◽

Optimal Algorithms ◽

Running Time ◽

Dynamic Programming Approach ◽

Programming Algorithms

We study competitions structured as hierarchically shaped single-elimination tournaments. We define optimal tournaments by maximizing attractiveness such that the topmost players will have the chance to meet in higher stages of the tournament. We propose a dynamic programming algorithm for computing optimal tournaments and we provide its sound complexity analysis. Based on the idea of the dynamic programming approach, we also develop more efficient deterministic and stochastic sub-optimal algorithms. We present experimental results obtained with the Python implementation of all the proposed algorithms regarding the optimality of solutions and the efficiency of the running time.

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

10.20944/preprints202006.0359.v1 ◽

2020 ◽

Cited By ~ 1

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.

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Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics

10.21203/rs.3.rs-1082732/v1 ◽

2021 ◽

Author(s):

Bertrand Marchand ◽

Yann Ponty ◽

Laurent Bulteau

Keyword(s):

Dynamic Programming ◽

Dynamic Programming Algorithm ◽

Tree Decomposition ◽

Structure Alignment ◽

Programming Algorithm ◽

Fixed Parameter Tractable ◽

Fpt Algorithms ◽

Graph Problems ◽

Time Space ◽

Diet Problem

Abstract Hard graph problems are ubiquitous in Bioinformatics, inspiring the design of specialized Fixed-Parameter Tractable algorithms, many of which rely on a combination of tree-decomposition and dynamic programming. The time/space complexities of such approaches hinge critically on low values for the treewidth tw of the input graph. In order to extend their scope of applicability, we introduce the Tree-Diet problem, i.e. the removal of a minimal set of edges such that a given tree-decomposition can be slimmed down to a prescribed treewidth tw. Our rationale is that the time gained thanks to a smaller treewidth in a parameterized algorithm compensates the extra post-processing needed to take deleted edges into account. Our core result is an FPT dynamic programming algorithm for Tree-Diet, using 2^O(tw)n time and space. We complement this result with parameterized complexity lower-bounds for stronger variants (e.g., NP-hardness when tw or tw − tw is constant). We propose a prototype implementation for our approach which we apply on difficult instances of selected RNA-based problems: RNA design, sequence-structure alignment, and search of pseudoknotted RNAs in genomes, revealing very encouraging results. This work paves the way for a wider adoption of tree-decomposition-based algorithms in Bioinformatics.

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Ubiquitous Wireless Power Transfer for Multiple Mobile Devices

10.5753/ctd.2021.15764 ◽

2021 ◽

Author(s):

Alexander Decker de Souza ◽

Luiz Filipe Menezes Vieira ◽

Marcos Augusto Menezes Vieira

Keyword(s):

Dynamic Programming ◽

Mobile Devices ◽

Linear Time ◽

Greedy Algorithms ◽

Dynamic Programming Algorithm ◽

Wireless Power Transfer ◽

Programming Algorithm ◽

Power Transfer ◽

Wireless Power ◽

Programming Algorithms

We propose two new computational problems associated with the charging of mobile devices using wireless power transfer via magnetic induction. Algorithms for these problems may enable ubiquitous charging, meaning the user is no longer required to be aware of the devices charging processes. We prove both problems as being NP-Hard and propose three dynamic programming algorithms to solve them in linear time regarding the size of the time horizon. We also propose three greedy algorithms for the problems. Experiments indicate that the best dynamic-programming algorithm among those proposed reaches between 89% and 97% of effectiveness, while the best greedy reaches between 74% and 92%, depending on the considered scenario.

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Cache efficient simple dynamic programming

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.3368 ◽

2005 ◽

Vol DMTCS Proceedings vol. AD,... (Proceedings) ◽

Author(s):

Cary Cherng ◽

Richard E. Ladner

Keyword(s):

Dynamic Programming ◽

Dynamic Programming Algorithm ◽

Recognition Algorithm ◽

Programming Algorithm ◽

Language Recognition ◽

International Audience ◽

Cache Efficient ◽

Programming Algorithms ◽

Context Free ◽

Cache Oblivious

International audience New cache-oblivious and cache-aware algorithms for simple dynamic programming based on Valiant's context-free language recognition algorithm are designed, implemented, analyzed, and empirically evaluated with timing studies and cache simulations. The studies show that for large inputs the cache-oblivious and cache-aware dynamic programming algorithms are significantly faster than the standard dynamic programming algorithm.

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