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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:

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compressing a single pdb

Compressing a Single PDB

Presented by: Danielle Sauer

CMPUT 652 Project

December 1, 2004

outline
Outline
  • Problem Definition
  • Key Background
  • Approach
  • Results
  • Conclusion
problem definition
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
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
Approach
  • Overview
  • Hash Functions
  • Puzzle Types
  • Domain Abstractions
overview of approach
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
Hash Functions
  • Three hash functions
    • Base 10 hash function
    • Perfect hash function (permutation)
    • Positional ordering hash function
base 10 and perfect hash
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
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
Puzzle Types
  • 8-puzzle from class
  • Pancake Puzzle
  • Topspin
  • Physical-based sliding tile puzzle
domain abstractions
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
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
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.
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