Solving the 24 Puzzle with Instance Dependent Pattern Databases

Abstract

A pattern database (PDB) is a heuristic function in a form of a lookup table which stores the cost of optimal solutions for instances of subproblems. These subproblems are generated by abstracting the entire search space into a smaller space called the pattern space. Traditionally, the entire pattern space is generated and each distinct pattern has an entry in the pattern database. Recently, [10] described a method for reducing pattern database memory requirements by storing only pattern database values for a specific instant of start and goal state thus enabling larger PDBs to be used and achieving speedup in the search. We enhance their method by dynamically growing the pattern database until memory is full, thereby allowing using any size of memory. We also show that memory could be saved by storing hierarchy of PDBs. Experimental results on the large 24 sliding tile puzzle show improvements of up to a factor of 40 over previous benchmark results [8].