Boosting search with variable elimination in constraint optimization and constraint satisfaction problems.

*(English)*Zbl 1057.68114Summary: There are two main solving schemas for constraint satisfaction and optimization problems: i) search, whose basic step is branching over the values of a variables, and ii) dynamic programming, whose basic step is variable elimination. Variable elimination is time and space exponential in a graph parameter called induced width, which renders the approach infeasible for many problem classes. However, by restricting variable elimination so that only low arity constraints are processed and recorded, it can be effectively combined with search, because the elimination of variables may reduce drastically the search tree size.

We introduce BE-BB(\(k\)), a hybrid general algorithm that combines search and variable elimination. The parameter \(k\) controls the tradeoff between the two strategies. The algorithm is space exponential in \(k\). Regarding time, we show that its complexity is bounded by \(k\) and a structural parameter from the constraint graph. We provide experimental evidence that the hybrid algorithm can outperform state-of-the-art algorithms in constraint satisfaction, Max-CSP and Weighted CSP. Especially in optimization tasks, the advantage of our approach over plain search can be overwhelming.

We introduce BE-BB(\(k\)), a hybrid general algorithm that combines search and variable elimination. The parameter \(k\) controls the tradeoff between the two strategies. The algorithm is space exponential in \(k\). Regarding time, we show that its complexity is bounded by \(k\) and a structural parameter from the constraint graph. We provide experimental evidence that the hybrid algorithm can outperform state-of-the-art algorithms in constraint satisfaction, Max-CSP and Weighted CSP. Especially in optimization tasks, the advantage of our approach over plain search can be overwhelming.

##### MSC:

68T20 | Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) |