Beyond Forks: Finding and Ranking Star Factorings for Decoupled Search

Star-topology decoupling is a recent search reduction method for forward state space search. The idea basically is to automatically identify a star factoring, then search only over the center component in the star, avoiding interleavings across leaf components. The framework can handle complex star topologies, yet prior work on decoupled search considered only factoring strategies identifying fork and inverted-fork topologies. Here, we introduce factoring strategies able to detect general star topologies, thereby extending the reach of decoupled search to new factorings and to new domains, sometimes resulting in significant performance improvements. Furthermore, we introduce a predictive portfolio method that reliably selects the most suitable factoring for a given planning task, leading to superior overall performance.

Tree Pruning for New Search Techniques in Computer Games

This paper proposes a new mechanism for pruning a search game tree in computer chess. The algorithm stores and then reuses chains or sequences of moves, built up from previous searches. These move sequences have a built-in forward-pruning mechanism that can radically reduce the search space. A typical search process might retrieve a move from a Transposition Table, where the decision of what move to retrieve would be based on the position itself. This algorithm stores move sequences based on what previous sequences were better, or caused cutoffs. The sequence is then returned based on the current move only. This is therefore position independent and could also be useful in games with imperfect information or uncertainty, where the whole situation is not known at any one time. Over a small set of tests, the algorithm was shown to clearly out perform Transposition Tables, both in terms of search reduction and game-play results. Finally, a completely new search process will be suggested for computer chess or games in general.

APPROXIMATE NEAREST NEIGHBOR SEARCH UNDER TRANSLATION INVARIANT HAUSDORFF DISTANCE

We present an embedding and search reduction which allow us to build the first data structure for the nearest neighbor search among small point sets with respect to the directed Hausdorff distance under translation. The search structure is non-heuristic in the sense that the quality of the results, the performance, and the space bound are guaranteed. Let n denote the number of point sets in the data base, s the maximal size of a point set, and d the dimension of the points. The nearest neighbor of a query point set under the translation invariant directed Hausdorff distance can be approximated by one or several nearest neighbor searches for single points in the Euclidean embedding space ℝd(s-1). The approximation factor is [Formula: see text] in case of even s and [Formula: see text] when s is odd. Depending on the direction of the Hausdorff distance either the number of queries or the space requirements are exponential in s. Furthermore it is shown how to find the exact nearest neighbor under the directed Hausdorff distance without transformation of the point sets within some weaker time and space bounds.