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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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