Abstract Zobrist Hashing: An Efficient Work Distribution Method for Parallel BestFirst Search Yuu Jinnai and Alex Fukunaga (The University of Tokyo) 1. Hash Distributed A* (HDA*) Hash Distributed A* (HDA*) is a parallel bestfirst graph search (A*) which distrbutes nodes according to a hash function which assigns each state to a unique process. As HDA* relies on the hash function for load balancing, the choice of hash function is crucial to its performance!
Summary
(Kishimoto et al. 2013)
We propose: Abstract Zobrist hashing, a hybrid of two strategies, which incorporates their strengths and alleviating their limitations. Main contribution: We showed that Abstract Zobrist hashing outperforms previous methods in slidingtile puzzle, MSA, and domainindependent classic planning.
Hash Distributed A*
H(s) = 1
Work Queue
Work Queue
process0
process1
load communication balance overhead
2. Previous Work Distribution Methods 2.1. Zobrist hashing (ZHDA*)
Goal: Distributes nodes uniformly while assigning neighbor nodes to the same process Method: Project features into abstract features and xor the hash value of each abstract feature
t1=2
1
2 t2=3
2
1
Strength: low communication overhead Limitation: worse load balance
Strength: good load balance Limitation: high communication overhead
×
3. Abstract Zobrist hashing (AZHDA*)
10101110
State
State Hash
process0
1 5 8
Abstraction
new!
AH(s) = R[A(s)]
2 t2=3
×
(Zhou and Hansen 2007; Burns et al 2010)
(Zhou and Hansen 2007; Burns et al. 2010) Goal: Assign neighbor nodes to the same process Method: Project nodes in the state space into abstract states, and abstract states are assigned to processors using a modulus operator.
ZH(s) = R[t1] xor R[t2] xor ... xor R[tn]
◯
(Zobrist 1970; Kishimoto et al 2013)
2.2. Abstraction (AHDA*)
(Zobrist 1970; Kishimoto et al. 2013) Goal: Distribute nodes uniformly among process Method: xor the hash value of each feature
Zobrist hashing
4 3 7
process1
1 5 8
2 6
t3=4
Init
Init
State
3
process0
process1
Communication Cost
process0
Communication Cost
process1
Feature
Abstract Feature
01100010
00101100
01010001
00011111
Abstract Feature Hash
State Hash
AZH Simultaneously address good load balance and communication overhead!
Goal
Goal
A(t2)=1
A(t3)=2
3
A(t1)=1
process0
Init
process1
4. Results on Slidingtile and Multiple Sequence Alignment
Search overhead (SO) := (#nodes expanded in parallel) / (#nodes expanded in sequential A*) Search overhead is caused by poor load balance.
0.3
0.9
0.25 0.2
0.8
0.5
process0
b16
AZHDA* AHDA* ZHDA* 4
6
10
#thread
12
1
14
0.8
0.2 10
#thread
12
14
15 Puzzle Walltime Efficiency
Z8 Z16
0.2
0.4
CO
0.6
0.8
1
A: AZHDA*, Z: ZHDA*, b: AHDA*
0.4
8
A16
24 Puzzle CO vs SO
0.6
6
Z4
A8
0 0
16
AZHDA* ZHDA* SafePBNF AHDA* PHDA*
4
A4
0.05 8
1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5
16
process1
Communication Cost
b4
0.1
24 Puzzle Walltime Efficiency
0
Goal
0.15
0.7 0.6
b8
SO
Efficiency
1
AZHDA* ZHDA* AHDA* HWD
Efficiency
Communication overhead (CO) := (#nodes sent to other processes) / (#nodes generated)
0.35
Efficiency
AZHDA* outperformed previous methods on 15puzzle, 24puzzle, and MSA, succeessfully mitigating communication overhead and achieving good load balance, while ZHDA* and AHDA* only succeeded in achieving either low CO or good load balancing.
4
6
8
10
#thread
12
14
MSA Walltime Efficiency
5. Results on DomainIndependent Planning AZHDA* achieved modest improvements over previous methods with automatically generated abstract features. #thread=8
16
Airport9 Barman11 Blocks102 Elevators1126 Floortile11 Freecell5 Gripper7 Logistics9832 PipesNoTk14 Sokoban1113 Transport0814 Visitall117Half Zenotravel8 Average Total
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