Nonserial Dynamic Programming and Tree Decomposition in Discrete Optimization

2007 ◽  
pp. 155-160 ◽  
Author(s):  
Oleg Shcherbina
Keyword(s):  
Dynamic Programming ◽  
Discrete Optimization ◽  
Tree Decomposition

scholarly journals Improving the Efficiency of Dynamic Programming on Tree Decompositions via Machine Learning

2017 ◽  
Vol 58 ◽  
pp. 829-858 ◽  
Author(s):  
Michael Abseher ◽  
Nysret Musliu ◽  
Stefan Woltran
Keyword(s):  
Machine Learning ◽  
Dynamic Programming ◽  
Tree Decomposition ◽  
Machine Learning Techniques ◽  
Problem Instance ◽  
Actual Problem ◽  
Learning Techniques ◽  
Tree Decompositions ◽  
Selection Of ◽  
General Method

Dynamic Programming (DP) over tree decompositions is a well-established method to solve problems - that are in general NP-hard - efficiently for instances of small treewidth. Experience shows that (i) heuristically computing a tree decomposition has negligible runtime compared to the DP step; and (ii) DP algorithms exhibit a high variance in runtime when using different tree decompositions; in fact, given an instance of the problem at hand, even decompositions of the same width might yield extremely diverging runtimes. We thus propose here a novel and general method that is based on selection of the best decomposition from an available pool of heuristically generated ones. For this purpose, we require machine learning techniques that provide automated selection based on features of the decomposition rather than on the actual problem instance. Thus, one main contribution of this work is to propose novel features for tree decompositions. Moreover, we report on extensive experiments in different problem domains which show a significant speedup when choosing the tree decomposition according to this concept over simply using an arbitrary one of the same width.

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

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.

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.

Branch and Tree Decomposition Techniques for Discrete Optimization

2005 ◽  
pp. 1-29 ◽  
Author(s):  
Illya V. Hicks ◽  
Arie M. C. A. Koster ◽  
Elif Kolotoğlu
Keyword(s):  
Discrete Optimization ◽  
Tree Decomposition ◽  
Decomposition Techniques

A Fuzzy Dynamic Programming Approach for the Mixed-Discrete Optimization of Mechanical Systems

2004 ◽  
Vol 127 (6) ◽  
pp. 1088-1099 ◽  
Author(s):  
Ying Xiong ◽  
Singiresu S. Rao
Keyword(s):  
Decision Making ◽  
Dynamic Programming ◽  
Discrete Optimization ◽  
Design Space ◽  
Optimization Problems ◽  
Mechanical Systems ◽  
Real Life ◽  
Programming Approach ◽  
Fuzzy Goal ◽  
Fuzzy State

Many engineering optimization problems can be considered as multistage decision-making problems. If the system involves uncertainty in the form of linguistic parameters and vague data, a fuzzy approach is to be used for its description. The solution of such problems can be accomplished through fuzzy dynamic programming. However, most of the existing fuzzy dynamic programming algorithms cannot deal with mixed-discrete design variables in the optimization of mechanical systems containing fuzzy information. They often assumed that a fuzzy goal is imposed only on the final state for simplicity, the values of fuzzy goal and other parameters need to be predefined, and an optimal solution is obtained in the continuous design space only. To better reflect the nature of uncertainties present in real-life optimization problems, a mixed-discrete fuzzy dynamic programming (MDFDP) approach is proposed in this work for solving multistage decision-making problems in mixed-discrete design space with a fuzzy goal and a fuzzy state imposed on each stage. The method can also be extended to solve general mixed-discrete fuzzy nonlinear programming problems if their corresponding crisp problems can be solved using dynamic programming approaches. The feasibility and versatility of the proposed method are illustrated by considering the design of a four-bar truss and the reliability-based optimization of a gearbox. To the authors’ knowledge, this work represents the first fuzzy dynamic programming method reported in the literature for dealing with mixed-discrete optimization problems.

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