1. Compressing a Single PDB Presented by: Danielle Sauer CMPUT 652 Project December 1, 2004

2. Outline  Problem Definition  Key Background  Approach  Results  Conclusion

3. Problem Definition  Motivation: What happens when a pattern database is too large to store in memory?  We can: Use several PDBs (and combine them into one). Compress individual PDBs.  My solution: Compress a single PDB.

4. Key Background  Pattern databases generally store two things: A state The state’s distance to goal.  The number of collisions are affected by: The hash function The size of the PDB

5. Approach  Overview  Hash Functions  Puzzle Types  Domain Abstractions

6. Overview of Approach  Stores only the distance in the PDB.  How to resolve collisions? Given state a i already in entry E in the PDB. State a j maps to entry E and collides with a i. Take the minimum distance value of a i and a j E = min(d i, d j )  Lossy compression (throwing away values).

7. Hash Functions  Three hash functions Base 10 hash function Perfect hash function (permutation) Positional ordering hash function

8. Base 10 and Perfect Hash  Base 10 Hash  Perfect Hash Function Based on permutations No gaps in the hash table No collisions 102 345 678 Go through each entry in the puzzle (row by row). Hashvalue = 102 345 678

9. Positional Ordering Hash  Ignore the nondistinct value with largest number of occurrences. 101 112 322 Position: 1 5 7 8 6 Tile #: 0 2 2 2 3 Hashvalue = 15786

10. Puzzle Types  8-puzzle from class  Pancake Puzzle  Topspin  Physical-based sliding tile puzzle

11. Domain Abstractions  1 “don’t care” symbol.  Maps a tile to itself or maps it to the “don’t care” symbol. d i (c) = cif c is an element of Gi blank if c = blank “don’t care” otherwise

12. Results  Expectation: As the size of the table becomes smaller, the number of nodes generated should become larger.  Reasoning: This method is lossy – we are throwing away heuristic values. The stored distance values will not be accurate heuristics for some of the states.

13. Expected Results

14. Preliminary Results

15. Summary  This method stores only the distance in the PDB.  It resolves collisions by storing the smallest distance of the colliding states.  Preliminary results suggest we can use a much smaller amount of memory and still get the same performance as a larger PDB.