CMPUT%20651:%20Front%20to%20Front%20Perimeter%20Search%20

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CMPUT 651Front to Front Perimeter Search
Pattern Databases

• Johnny Huynh

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Outline

• Introduction to FFPS
• Problems
• Improving FFPS itself
• Perimeters and PDBs
• Results
• Conclusion

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Front-to-Front Perimeter Search (FFPS)

• Build a perimeter around goal
• Find shortest path a perimeter state
• Use a heuristic to find a perimeter state
• Heuristic can be a pattern database (PDB)

P
S
G
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Problems with FFPS

• Taking the MIN of estimates
• Checking for P Perimeter States
• Each node expansion requires P estimates
• Perimeter states and PDBs requires memory

P
S
G
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Problems with FFPS

• Taking the MIN of estimates
• Checking for P Perimeter States
• Each node expansion requires P estimates
• Perimeter states and PDBs requires memory

P
S
G
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Improving FFPSReducing Perimeter Checks

• given a perimeter state, p,
• if h(p) 0
• then state, s, needs to be checked only when
• h(s) 0.
• In the 9-puzzle (2x5), reduced number of goal
  comparisons by 92.5

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Problems with FFPS

• Taking the MIN of estimates
• Checking for P Perimeter States
• Each node expansion requires P estimates
• Perimeter states and PDBs requires memory

P
S
G
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Improving FFPSReducing Heuristic Evaluations

• Fraction of Node expansion time required to
  evaluate heuristic determines speedup.
• Dillenburg 93

fraction Optimal Radius Speedup
0.01 6 4.6
0.02 5 3.3
0.05 4 2.2
0.1 3 1.6
0.2 2 1.2
0.3 1 1.1
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Improving FFPSReducing Heuristic Evaluations

• If heuristic is monotonically non-decreasing.
• Estimate distance to all perimeter states
• Decrease estimate by edge cost
• Re-compute only the minimum estimates

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Improving FFPSReducing Heuristic Evaluations
Radius Total PDB Lookups Reduced PDB Lookups
1 9,910 427 95.7
2 743,432 46,175 93.8
3 1,556,360 129,770 91.7
4 2,615,490 256,375 90.2
5 3,644,070 405,560 88.9
6 1,529,750 168,845 88.9
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Problems with FFPS

• Taking the MIN of estimates
• Checking for P Perimeter States
• Each node expansion requires P estimates
• Perimeter states and PDBs requires memory

P
S
G
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Memory for Perimeter or PDB?

• Distance to each P estimated by a PDB
• Fixing number of states in memory,
• How many Perimeter states?
• How many PDB entries?
• P P PDB c
• Must remember that PDB determined by level of
  abstraction

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Initial (Poor) Results
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Initial (Poor) Results
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Mixing Levels of Abstraction

• c P P PDB
• What if P gt PDB?
• Each Perimeters PDB doesnt have to be the same
• c P ?(Pi PDBi) , Pi ? P , PDBi ? PDB

Abstraction PDBi
P0 011234567 180k
P1 011223456 90k
P2 011123456 60k
P2 011122345 30k
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Mixing Levels of Abstraction
Averages Same Level of Abstraction (PDB 90k) Different Levels of Abstraction (avg PDB 90k)
Abstraction0 Look-ups 170 21
Abstraction1 Look-ups 144 156
Abstraction2 Look-ups 109 239
Abstraction3 Look-ups 133 250
Nodes Expanded 56.2 64.5

• 8-puzzle with 8 perimeter nodes and 360K states
  in memory

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Combining Perimeter PDBs

• If each PDB uses same abstraction, then will
  look up the same key in each PDB.
• h(s) min PDB1 F(s) PDBN F(s)
• Create one PDB with the same keys, and save only
  the MIN from each perimeter PDB.
• h(s) PDBcF(s)
• Reduce memory from
• P P PDB to P PDB

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Combining Perimeter PDBs
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Combining Perimeter PDBs
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10-pancake results
Radius Nodes Expanded Elapsed Time (s)
0 69565 12.664
1 53675 9.936
2 37751 6.994
3 24152 4.476
4 12822 2.485
5 5290 1.051
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Conclusion

• FFPS performance affected by
• Number of goal comparisons
• Number of heuristic evaluations (PDB lookups)
• FFPS Perimeter vs PDB
• Without combining PDBs, radius should be kept
  small.
• Combining PDBs, memory should be allocated for
  radius (up to a certain point?)

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Questions?