A Theoretical Evaluation of Selected Backtracking Algorithms
نویسندگان
چکیده
In recent years, many new backtracking algorithms for solving constraint satisfaction problems have been proposed. The algorithms are usually evaluated by empirical testing. This method, however, has its limitations. Our paper adopts a different, purely theoretical approach, which is based on characterizations of the sets of search tree nodes visited by the backtracking algorithms. A notion of inconsistency between instantiations and variables is introduced, and is shown to be a useful tool for characterizing such well-known concepts as backtrack, backjump, and domain annihilation. The characterizations enable us to: (a) prove the correctness of the algorithms, and (b) partially order the algorithms according to two standard performance measures: the number of nodes visited, and the number of consistency checks performed. Among other results, we prove the correctness of Backjumping and Conflict-Directed Backjumping, and show that Forward Checking never visits more nodes than Backjumping. Our approach leads us also to propose a modification to two hybrid backtracking algorithms, Backmarking with Backjumping (BMJ) and Backmarking with Conflict-Directed Backjumping (BM-CBJ), so that they always perform fewer consistency checks than the original algorithms.
منابع مشابه
Looking Forward in Constraint Satisfaction Algorithms
Empirical evidence indicates that the most successful backtracking algorithms for solving constraint satisfaction problems do some level of forward constraint propagation. That is they check constraints against the as yet uninstantiated variables in the search tree. Two popular examples are the forward checking and maintaining arc-consistency algorithms. Although there is a growing body of empi...
متن کاملEvolutionary Algorithms Combined with Deterministic Search
This paper provides insight into combining stochastic and deterministic search methods using evolutionary algorithms (EAs) such as evolutionary programming, evolutionary strategies, and genetic algorithms integrated with depth-rst search with backtracking, branch and bound, and best-rst search algorithms such as A. An important view of such an integration focuses on both theoretical analysis an...
متن کاملPropositional satisfiability: Techniques, algorithms and applications
Recent years have seen remarkable progress in propositional satisfiability (SAT), with significant theoretical and practical contributions. Algorithmic solutions for SAT include, among others, local search, backtrack search and formula manipulation techniques. Despite the worst-case exponential run time of all known algorithms, SAT solvers can currently be used to solve hard benchmark problems....
متن کاملOn Backtracking in Real-time Heuristic Search
Real-time heuristic search algorithms are suitable for situated agents that need to make their decisions in constant time. Since the original work by Korf nearly two decades ago, numerous extensions have been suggested. One of the most intriguing extensions is the idea of backtracking wherein the agent decides to return to a previously visited state as opposed to moving forward greedily. This i...
متن کاملRetroactive Ordering for Dynamic Backtracking
Dynamic Backtracking (DBT ) is a well known algorithm for solving Constraint Satisfaction Problems. In DBT , variables are allowed to keep their assignment during backjump, if they are compatible with the set of eliminating explanations. A previous study has shown that when DBT is combined with variable ordering heuristics it performs poorly compared to standard Conflictdirected Backjumping (CB...
متن کامل