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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

• Problem Definition

• Key Background

• Approach

• Results

• Conclusion

• 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.

• 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

• Overview

• Hash Functions

• Puzzle Types

• Domain Abstractions

• 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).

• Three hash functions

• Base 10 hash function

• Perfect hash function (permutation)

• Positional ordering hash function

• 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

• Ignore the nondistinct value with largest number of occurrences.

Position: 1 5 7 8 6

Tile #: 0 2 2 2 3

Hashvalue = 15786

• 8-puzzle from class

• Pancake Puzzle

• Topspin

• Physical-based sliding tile puzzle

• 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

• 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.

• 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.