Compressing a Single PDB

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# Compressing a Single PDB - PowerPoint PPT Presentation

Compressing a Single PDB. Presented by: Danielle Sauer CMPUT 652 Project December 1, 2004. Outline. Problem Definition Key Background Approach Results Conclusion. Problem Definition. Motivation: What happens when a pattern database is too large to store in memory? We can:

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### Compressing a Single PDB

Presented by: Danielle Sauer

CMPUT 652 Project

December 1, 2004

Outline
• Problem Definition
• Key Background
• Approach
• Results
• Conclusion
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.
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
Approach
• Overview
• Hash Functions
• Puzzle Types
• Domain Abstractions
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).
Hash Functions
• Three hash functions
• Base 10 hash function
• Perfect hash function (permutation)
• Positional ordering hash function
Base 10 and Perfect Hash
• Base 10 Hash
• Perfect Hash Function
• Based on permutations
• No gaps in the hash table
• No collisions

Go through each entry in the puzzle (row by row).

Hashvalue = 102 345 678

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

Puzzle Types
• 8-puzzle from class
• Pancake Puzzle
• Topspin
• Physical-based sliding tile puzzle
Domain Abstractions
• 1 “don’t care” symbol.
• Maps a tile to itself or maps it to the “don’t care” symbol.

di(c) = c if c is an element of Gi

blank if c = blank

“don’t care” otherwise

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.
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.