Additive Pattern Database Heuristics

TL;DR

This paper introduces additive pattern database heuristics, both static and dynamic, for search problems, demonstrating their effectiveness across multiple domains like sliding-tile puzzles, Towers of Hanoi, and graph vertex cover.

Contribution

It extends pattern database heuristics to include static and dynamic partitioning methods, applicable to various problem domains, improving heuristic accuracy and search efficiency.

Findings

Static partitioning works best in some domains.

Dynamic partitioning outperforms in others.

Both methods yield the best known heuristics for tested problems.

Abstract

We explore a method for computing admissible heuristic evaluation functions for search problems. It utilizes pattern databases, which are precomputed tables of the exact cost of solving various subproblems of an existing problem. Unlike standard pattern database heuristics, however, we partition our problems into disjoint subproblems, so that the costs of solving the different subproblems can be added together without overestimating the cost of solving the original problem. Previously, we showed how to statically partition the sliding-tile puzzles into disjoint groups of tiles to compute an admissible heuristic, using the same partition for each state and problem instance. Here we extend the method and show that it applies to other domains as well. We also present another method for additive heuristics which we call dynamically partitioned pattern databases. Here we partition the problem into disjoint subproblems for each state of the search dynamically. We discuss the pros and cons of each of these methods and apply both methods to three different problem domains: the sliding-tile puzzles, the 4-peg Towers of Hanoi problem, and finding an optimal vertex cover of a graph. We find that in some problem domains, static partitioning is most effective, while in others dynamic partitioning is a better choice. In each of these problem domains, either statically partitioned or dynamically partitioned pattern database heuristics are the best known heuristics for the problem.