scholarly journals Dynamic Programming Algorithms for Computing Optimal Knockout Tournaments

Mathematics ◽  
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.

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 DYNAFOLD: A DYNAMIC PROGRAMMING APPROACH TO PROTEIN BACKBONE STRUCTURE DETERMINATION FROM MINIMAL SETS OF RESIDUAL DIPOLAR COUPLINGS

2014 ◽  
Vol 12 (01) ◽  
pp. 1450002 ◽  
Author(s):  
RISHI MUKHOPADHYAY ◽  
STEPHANIE IRAUSQUIN ◽  
CHRISTOPHER SCHMIDT ◽  
HOMAYOUN VALAFAR
Keyword(s):  
Dynamic Programming ◽  
Structure Determination ◽  
Residual Dipolar Couplings ◽  
Dynamic Programming Algorithm ◽  
Synthetic Data ◽  
Dipolar Couplings ◽  
Programming Algorithm ◽  
Programming Approach ◽  
Protein Backbone ◽  
Minimal Sets

Residual Dipolar Couplings (RDCs) are a source of NMR data that can provide a powerful set of constraints on the orientation of inter-nuclear vectors, and are quickly becoming a larger part of the experimental toolset for molecular biologists. However, few reliable protocols exist for the determination of protein backbone structures from small sets of RDCs. DynaFold is a new dynamic programming algorithm designed specifically for this task, using minimal sets of RDCs collected in multiple alignment media. DynaFold was first tested utilizing synthetic data generated for the N – H , C α– H α, and C – N vectors of 1BRF, 1F53, 110M, and 3LAY proteins, with up to ±1 Hz error in three alignment media, and was able to produce structures with less than 1.9 Å of the original structures. DynaFold was then tested using experimental data, obtained from the Biological Magnetic Resonance Bank, for proteins PDBID:1P7E and 1D3Z using RDC data from two alignment media. This exercise yielded structures within 1.0 Å of their respective published structures in segments with high data density, and less than 1.9 Å over the entire protein. The same sets of RDC data were also used in comparisons with traditional methods for analysis of RDCs, which failed to match the accuracy of DynaFold's approach to structure determination.

scholarly journals ON RECTANGULAR COVERING PROBLEMS

2009 ◽  
Vol 19 (04) ◽  
pp. 325-340
Author(s):  
STEFAN PORSCHEN
Keyword(s):  
Dynamic Programming ◽  
Objective Function ◽  
Structural Features ◽  
Programming Approach ◽  
Dynamic Programming Approach ◽  
Deterministic Algorithms ◽  
Cost Constraints ◽  
Solution Methods ◽  
Finite Space ◽  
Programming Algorithms

Many applications like image processing, data compression or pattern recognition require a covering of a set of n points most often located in the (discrete) plane by rectangles due to specific cost constraints. In this paper we provide exact dynamic programming algorithms for covering point sets by regular rectangles, that have to obey certain boundary conditions, namely all rectangles must have lengths of at least k, which is a prescribed problem parameter. The concrete objective function underlying our optimization problem is the sum of area, circumference and a constant over all rectangles forming a covering. This objective function can be motivated by requirements of numerically solving PDE's by discretization over (adaptive multi-)grids. More precisely, we propose exact deterministic algorithms for such problems based on a (set theoretic) dynamic programming approach yielding a time bound of O(n23n). In a second step this bound is (asymptotically) decreased to O(n62n) by exploiting some structural features. Finally, a generalization of the problem and its solution methods is discussed for the case of arbitrary (finite) space dimension.

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.

RANKING VALID TOPOLOGIES OF THE SECONDARY STRUCTURE ELEMENTS USING A CONSTRAINT GRAPH

2011 ◽  
Vol 09 (03) ◽  
pp. 415-430 ◽  
Author(s):  
KAMAL AL NASR ◽  
DESH RANJAN ◽  
MOHAMMAD ZUBAIR ◽  
JING HE
Keyword(s):  
Dynamic Programming ◽  
Secondary Structure ◽  
Protein Complexes ◽  
Dynamic Programming Algorithm ◽  
Weighted Graph ◽  
Minimum Cost ◽  
Programming Algorithm ◽  
Programming Approach ◽  
Constraint Graph ◽  
Density Maps

Electron cryo-microscopy is a fast advancing biophysical technique to derive three-dimensional structures of large protein complexes. Using this technique, many density maps have been generated at intermediate resolution such as 6–10 Å resolution. Although it is challenging to derive the backbone of the protein directly from such density maps, secondary structure elements such as helices and β-sheets can be computationally detected. Our work in this paper provides an approach to enumerate the top-ranked possible topologies instead of enumerating the entire population of the topologies. This approach is particularly practical for large proteins. We developed a directed weighted graph, the topology graph, to represent the secondary structure assignment problem. We prove that the problem of finding the valid topology with the minimum cost is NP hard. We developed an O(N2 2N) dynamic programming algorithm to identify the topology with the minimum cost. The test of 15 proteins suggests that our dynamic programming approach is feasible to work with proteins of much larger size than we could before. The largest protein in the test contains 18 helical sticks detected from the density map out of 33 helices in the protein.

scholarly journals The dynamic programming approach to long term production planning in agriculture

2011 ◽  
Vol 59 (2) ◽  
pp. 129-136 ◽  
Author(s):  
Jitka Janová
Keyword(s):  
Dynamic Programming ◽  
Production Planning ◽  
Programming Model ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Goal Function ◽  
Programming Algorithm ◽  
Programming Approach ◽  
Model Case ◽  
Local Character

The production planning in agriculture is one of the most important decision problems of the farmer. Although some decision support tools based mainly on linear programming and addressed to agriculture authorities were presented, their direct application by a farmer is not possible. This is mainly due to the local character of the models developed for particular agricultural conditions and also due to the complexness of underlying mathematical programming models.This paper aims to develop dynamic programming model for the long run crop plan optimization covering the typical conditions of Czech farms, which could serve as a platform for further enlargements and changes according to needs and conditions of particular farm. The dynamic programming algorithm is developed in detail for model case of four areas to be planted by four crops each year. The possibility of covering different constraints by generating the state space is discussed, and the generating procedure for crop rotation rules is shown. The goal function reflects the farmers objective of profit maximization and it is defined with respect to harvests’ randomness. The case study is solved for the data from South Moravian agriculture cooperative and the optimal solution is presented and discussed.

scholarly journals Ubiquitous Wireless Power Transfer for Multiple Mobile Devices

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.

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

2012 ◽  
Vol 12 (4-5) ◽  
pp. 445-464 ◽  
Author(s):  
BERNHARD BLIEM ◽  
MICHAEL MORAK ◽  
STEFAN WOLTRAN
Keyword(s):  
Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Answer Set Programming ◽  
Tree Decomposition ◽  
Programming Algorithm ◽  
Technical Details ◽  
Local Solutions ◽  
Tree Decompositions ◽  
Programming Algorithms ◽  
Answer Set

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.

scholarly journals Cache efficient simple dynamic programming

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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