Value Compression of Pattern Databases

One common pattern database compression technique is to merge adjacent database entries and store the minimum of merged entries to maintain heuristic admissibility. In this paper we propose a compression technique that preserves every entry, but reduces the number of bits used to store each entry, therefore limiting the values that can be represented. Even when this technique throws away low values in the heuristic, it can still have better performance than the traditional approach. We develop a theoretical basis for selecting which values to keep and show improved performance in both unidirectional and bidirectional search

Merge-and-shrink abstractions for classical planning : theory, strategies, and implementation

Classical planning is the problem of finding a sequence of deterministic actions in a state space that lead from an initial state to a state satisfying some goal condition. The dominant approach to optimally solve planning tasks is heuristic search, in particular A* search combined with an admissible heuristic. While there exist many different admissible heuristics, we focus on abstraction heuristics in this thesis, and in particular, on the well-established merge-and-shrink heuristics. Our main theoretical contribution is to provide a comprehensive description of the merge-and-shrink framework in terms of transformations of transition systems. Unlike previous accounts, our description is fully compositional, i.e. can be understood by understanding each transformation in isolation. In particular, in addition to the name-giving merge and shrink transformations, we also describe pruning and label reduction as such transformations. The latter is based on generalized label reduction, a new theory that removes all of the restrictions of the previous definition of label reduction. We study the four types of transformations in terms of desirable formal properties and explain how these properties transfer to heuristics being admissible and consistent or even perfect. We also describe an optimized implementation of the merge-and-shrink framework that substantially improves the efficiency compared to previous implementations. Furthermore, we investigate the expressive power of merge-and-shrink abstractions by analyzing factored mappings, the data structure they use for representing functions. In particular, we show that there exist certain families of functions that can be compactly represented by so-called non-linear factored mappings but not by linear ones. On the practical side, we contribute several non-linear merge strategies to the merge-and-shrink toolbox. In particular, we adapt a merge strategy from model checking to planning, provide a framework to enhance existing merge strategies based on symmetries, devise a simple score-based merge strategy that minimizes the maximum size of transition systems of the merge-and-shrink computation, and describe another framework to enhance merge strategies based on an analysis of causal dependencies of the planning task. In a large experimental study, we show the evolution of the performance of merge-and-shrink heuristics on planning benchmarks. Starting with the state of the art before the contributions of this thesis, we subsequently evaluate all of our techniques and show that state-of-the-art non-linear merge-and-shrink heuristics improve significantly over the previous state of the art

On Variable Dependencies and Compressed Pattern Databases

Pattern databases are among the strongest known heuristics for many classical search benchmarks such as sliding-tile puzzles, the 4-peg Towers of Hanoi puzzles, Rubik's Cube, and TopSpin. Min-compression is a generally applicable technique for augmenting pattern database heuristics that has led to marked experimental improvements in some settings, while being ineffective in others. We provide a theoretical explanation for these experimental phenomena by studying the interaction between the ranking function used to order abstract states in a pattern database, the compression scheme used to abstract states, and the dependencies between state variables in the problem representation