Compressing a Single PDB

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 states 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 ai already in entry E in the PDB.
• State aj maps to entry E and collides with ai.
• Take the minimum distance value of ai and aj
• E min(di, dj)
• 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

1 0 2
3 4 5
6 7 8
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.

Position 1 5 7 8 6 Tile 0 2 2 2
3 Hashvalue 15786
1 0 1
1 1 2
3 2 2
10
Puzzle Types

• 8-puzzle from class
• Pancake Puzzle
• Topspin
• Physical-based sliding tile puzzle

11
Domain Abstractions

• 1 dont care symbol.
• Maps a tile to itself or maps it to the dont
  care symbol.
• di(c) c if c is an element of Gi
• blank if c blank
• dont 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.