Perimeter Search Performance

Abstract

The idea of bidirectional search has fascinated researchers for years: large gains seem intuitively possible because of the exponential growth of search trees. Furthermore, some researchers report significant gains for bidirectional search strategies. This is all the more frustrating for those practitioners that have failed to realize the promised improvements.

We suggest a model for perimeter search performance that, instead of simply counting nodes, counts the execution of important algorithmic subtasks and weights them with their runtime. We then use this model to predict total runtimes of perimeter search algorithms more accurately. Our model conforms to the observation that unidirectional search (IDA*) is a special case of its bidirectional counterpart, perimeter search (BIDA*), with a perimeter depth of 0. Using this insight, we can determine the optimal perimeter depth for BIDA* a priori, thus allowing BIDA* to subsume IDA*.

Our model forecasts that applications with expensive heuristic functions have little if anything to gain from perimeter search. Unfortunately, expensive heuristics are often used by high-performance programs. Our experiments show that on the 15-puzzle perimeter search narrowly outperforms its unidirectional counterpart. This finding is consistent with the literature and our model. However, it does not appear that a state-of-the-art implementation of a 15-puzzle solver can benefit from the perimeter search strategy.