6,670 research outputs found
Intelligent search strategies based on adaptive Constraint Handling Rules
The most advanced implementation of adaptive constraint processing with
Constraint Handling Rules (CHR) allows the application of intelligent search
strategies to solve Constraint Satisfaction Problems (CSP). This presentation
compares an improved version of conflict-directed backjumping and two variants
of dynamic backtracking with respect to chronological backtracking on some of
the AIM instances which are a benchmark set of random 3-SAT problems. A CHR
implementation of a Boolean constraint solver combined with these different
search strategies in Java is thus being compared with a CHR implementation of
the same Boolean constraint solver combined with chronological backtracking in
SICStus Prolog. This comparison shows that the addition of ``intelligence'' to
the search process may reduce the number of search steps dramatically.
Furthermore, the runtime of their Java implementations is in most cases faster
than the implementations of chronological backtracking. More specifically,
conflict-directed backjumping is even faster than the SICStus Prolog
implementation of chronological backtracking, although our Java implementation
of CHR lacks the optimisations made in the SICStus Prolog system. To appear in
Theory and Practice of Logic Programming (TPLP).Comment: Number of pages: 27 Number of figures: 14 Number of Tables:
Planning Graph as a (Dynamic) CSP: Exploiting EBL, DDB and other CSP Search Techniques in Graphplan
This paper reviews the connections between Graphplan's planning-graph and the
dynamic constraint satisfaction problem and motivates the need for adapting CSP
search techniques to the Graphplan algorithm. It then describes how explanation
based learning, dependency directed backtracking, dynamic variable ordering,
forward checking, sticky values and random-restart search strategies can be
adapted to Graphplan. Empirical results are provided to demonstrate that these
augmentations improve Graphplan's performance significantly (up to 1000x
speedups) on several benchmark problems. Special attention is paid to the
explanation-based learning and dependency directed backtracking techniques as
they are empirically found to be most useful in improving the performance of
Graphplan
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Experimental evaluation of preprocessing algorithms for constraint satisfaction problems
This paper presents an experimental evaluation of two orthogonal schemes for preprocessing constraint satisfaction problems (CSPs). The first of these schemes involves a class of local consistency techniques that includes directional arc consistency, directional path consistency, and adaptive consistency. The other scheme concerns the prearrangement of variables in a linear order to facilitate an efficient search. In the first series of experiments, we evaluated the effect of each of the local consistency techniques on backtracking and its common enhancement, backjumping. Surprizingly, although adaptive consistency has the best worst-case complexity bounds, we have found that it exhibits the worst performance, unless the constraint graph was very sparse. Directional arc consistency (followed by either backjumping or backtracking) and backjumping (without any pre-processing) outperformed all other techniques; moreover, the former dominated the latter in computationally intensive situations. The second series of experiments suggests that maximum cardinality and minimum width arc the best pre-ordering (i.e., static ordering) strategies, while dynamic search rearrangement is superior to all the preorderings studied
Heuristic Backtracking Algorithms for SAT
In recent years backtrack search SAT solvers have been the subject of dramatic improvements. These improvements allowed SAT solvers to successfully replace BDDs in many areas of formal verification, and also motivated the development of many new challenging problem instances, many of which too hard for the current generation of SAT solvers. As a result, further improvements to SAT technology are expected to have key consequences in formal verification. The objective of this paper is to propose heuristic approaches to the backtrack step of backtrack search SAT solvers, with the goal of increasing the ability of the SAT solver to search different parts of the search space. The proposed heuristics to the backtrack step are inspired by the heuristics proposed in recent years for the branching step of SAT solvers, namely VSIDS and some of its improvements. The preliminary experimental results are promising, and motivate the integration of heuristic backtracking in state-of-the-art SAT solvers. 1
GRASP: A New Search Algorithm for Satisfiability
This paper introduces GRASP (Generic search Algorithm J3r the Satisfiabilily Problem), an integrated algorithmic J3amework 30r SAT that unifies several previously proposed searchpruning techniques and jcilitates identification of additional ones. GRASP is premised on the inevitability of conflicts during search and its most distinguishingjature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by 'ecording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Einally, straighrward bookkeeping of the causali y chains leading up to conflicts a/lows GRASP to identij) assignments that are necessary jr a solution to be found. Experimental results obtained jom a large number of benchmarks, including many J3om the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely ejctive jr a large number of representative classes of SAT instances
An Overview of Backtrack Search Satisfiability Algorithms
Propositional Satisfiability (SAT) is often used as the underlying model for a significan
Enhancing a Search Algorithm to Perform Intelligent Backtracking
This paper illustrates how a Prolog program, using chronological backtracking
to find a solution in some search space, can be enhanced to perform intelligent
backtracking. The enhancement crucially relies on the impurity of Prolog that
allows a program to store information when a dead end is reached. To illustrate
the technique, a simple search program is enhanced.
To appear in Theory and Practice of Logic Programming.
Keywords: intelligent backtracking, dependency-directed backtracking,
backjumping, conflict-directed backjumping, nogood sets, look-back.Comment: To appear in Theory and Practice of Logic Programmin
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
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