The Grid-Based Path Planning Competition
Transcript of The Grid-Based Path Planning Competition
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
The Grid-Based Path Planning Competition
-or-Contractions, contractions everywhere
Nathan R. SturtevantUniversity of Denver
Symposium on Combinatorial SearchJune 13, 2015
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Testing Heuristics• Suppose: bright idea for a new algorithm
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Testing Heuristics• Suppose: bright idea for a new algorithm• Test on a standard set of benchmark problems
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Testing Heuristics• Suppose: bright idea for a new algorithm• Test on a standard set of benchmark problems
• If the new algorithm wins︎:
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Testing Heuristics• Suppose: bright idea for a new algorithm• Test on a standard set of benchmark problems
• If the new algorithm wins︎:• The work is submitted for publication︎
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Testing Heuristics• Suppose: bright idea for a new algorithm• Test on a standard set of benchmark problems
• If the new algorithm wins︎:• The work is submitted for publication︎
• Otherwise it is written o ︎ff as a failure
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Testing Heuristics• Suppose: bright idea for a new algorithm• Test on a standard set of benchmark problems
• If the new algorithm wins︎:• The work is submitted for publication︎
• Otherwise it is written o ︎ff as a failure
• Approach “spawns a host of evils”
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Complaints
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Complaints• The emphasis on competition is fundamentally anti︎intellectual• Does not build the sort of insight…(for)…more effective algorithms
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Complaints• The emphasis on competition is fundamentally anti︎intellectual• Does not build the sort of insight…(for)…more effective algorithms
• Competition diverts time and resources from productive investigation• Hours spent crafting the fastest possible code
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Example• 2nd DIMACS challenge
• Studied SAT problems• Stimulated great interest• Difficult to know why one approach is better
• Studies which tease out why approaches work without performance increase are hard to publish, but important intellectually
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Conclusion• New norms for research:
• “That experimental results be evaluated on the basis of whether they contribute to our understanding︎ rather than whether they show that the author ︎s algorithm can win a race with the state of the art.”
• Algorithm researchers shouldn’t have the “burden of exhibiting faster and better algorithms in each paper.”
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Talk Goals• Present latest GPPC results
• Present insights into commonalities in approaches
• Discuss future challenges
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Recent (related) example• 9th DIMACS challenge
• Begun in 2005• Path planning on road networks
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Result of Challenge• Road networks for testing made available
• 200k to 24 million nodes• 700k to 60 million edges
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
• Better Heuristics:• Computing the shortest path: A search meets graph theory [Goldberg & Harrelson, 2005]
• Better Bounding:• Better Landmarks Within Reach [Goldberg et. al., 2007]
• Exploiting Structure:• In Transit to Constant Time Shortest-Path Queries in Road Networks [Bast et. al. 2007]
• Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks [Geisberger et. al. 2008]
• A Hub-Based Labeling Algorithm for Shortest Paths in Road Networks [Abraham et. al., 2011]
• Theoretical Justification:• Highway Dimension, Shortest Paths, and Provably Efficient Algorithms [Abraham et. al., 2010]
Result of Challenge
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Observation
Benchmark data spurs research
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Observation
Benchmark data spurs research
Imperfect benchmarks are better than no benchmarks.
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Observation
Benchmark data spurs research
Imperfect benchmarks are better than no benchmarks.
You have to have (flawed) benchmarks before you can fix/improve them.
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Grid Map Benchmarks• Between Fall 2006 - Dec. 2008 consulted with BioWare on Dragon Age: Origins
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Grid Map Benchmarks• Between Fall 2006 - Dec. 2008 consulted with BioWare on Dragon Age: Origins• They agreed to allow free distribution of map data!
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Grid Map Benchmarks• Between Fall 2006 - Dec. 2008 consulted with BioWare on Dragon Age: Origins• They agreed to allow free distribution of map data!
• Combined with other sources to form the “movingai” grid map repository
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Grid Map Benchmarks• Between Fall 2006 - Dec. 2008 consulted with BioWare on Dragon Age: Origins• They agreed to allow free distribution of map data!
• Combined with other sources to form the “movingai” grid map repository• [Sturtevant, 2012]
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Grid-Based PathPlanning Competition
• Started in 2012; goals to:• Improve evaluation• Establish metrics• Improve comparisons
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Entry Specification• Time allowed for pre-processing• At runtime:
• Load pre-processed data• Path query (start, goal) given to entry
• Entry returns full or partial path• Query repeated until full path returned
• Run 5 times for statistical significance
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Problem SetupSource # Maps # Problems
Starcraft 11 29,970
Dragon Age: Origins 27 44,414
Dragon Age 2 57 54,360
Mazes 18 145,976
Random 18 32,228
Rooms 18 27,130
Total 132 347,868
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Dragon Age 2Dragon Age: OriginsStarcraftRandomMazeRoom
Map
Cou
nt
0
10
20
Map Size (# free cells)102 103 104 105 106 107
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Dragon Age 2Dragon Age: OriginsStarcraftRandomMazeRoom
Map
Cou
nt
0
10
20
Map Size (# free cells)102 103 104 105 106 107
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Dragon Age 2Dragon Age: OriginsStarcraftRandomMazeRoom
Map
Cou
nt
0
10
20
Map Size (# free cells)102 103 104 105 106 107
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Dragon Age 2Dragon Age: OriginsStarcraftRandomMazeRoom
Map
Cou
nt
0
10
20
Map Size (# free cells)102 103 104 105 106 107
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Metrics• Total/average time to solve problem set
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Metrics• Total/average time to solve problem set• Time for 20 steps (real-time startup)
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Metrics• Total/average time to solve problem set• Time for 20 steps (real-time startup)• Maximum segment time (real-time steady state)
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Metrics• Total/average time to solve problem set• Time for 20 steps (real-time startup)• Maximum segment time (real-time steady state)• Suboptimality
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Metrics• Total/average time to solve problem set• Time for 20 steps (real-time startup)• Maximum segment time (real-time steady state)• Suboptimality• Correctness
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Metrics• Total/average time to solve problem set• Time for 20 steps (real-time startup)• Maximum segment time (real-time steady state)• Suboptimality• Correctness• RAM at runtime (before/after)
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Metrics• Total/average time to solve problem set• Time for 20 steps (real-time startup)• Maximum segment time (real-time steady state)• Suboptimality• Correctness• RAM at runtime (before/after)• Disk storage
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Metrics• Total/average time to solve problem set• Time for 20 steps (real-time startup)• Maximum segment time (real-time steady state)• Suboptimality• Correctness• RAM at runtime (before/after)• Disk storage• Pre-computation
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
All 2014 Approaches• Single-Row Compression (SRC) (4 variants)
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
All 2014 Approaches• Single-Row Compression (SRC) (4 variants) • Contraction Hierarchies (CH)
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
All 2014 Approaches• Single-Row Compression (SRC) (4 variants) • Contraction Hierarchies (CH) • N-level Subgoals
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
All 2014 Approaches• Single-Row Compression (SRC) (4 variants) • Contraction Hierarchies (CH) • N-level Subgoals• JPS+, JPS+ Bucket, A* Bucket
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
All 2014 Approaches• Single-Row Compression (SRC) (4 variants) • Contraction Hierarchies (CH) • N-level Subgoals• JPS+, JPS+ Bucket, A* Bucket• BLJPS (2 variants), BLJPS_Subgoal
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
All 2014 Approaches• Single-Row Compression (SRC) (4 variants) • Contraction Hierarchies (CH) • N-level Subgoals• JPS+, JPS+ Bucket, A* Bucket• BLJPS (2 variants), BLJPS_Subgoal• Relaxed A*, Relaxed A* Subgoal
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Single Row Compression• Ben Strasser [KIT], Adi Botea [IBM Dublin], and Daniel Harabor [NICTA]• Build full all-pairs-shortest-path data• Run-length encoding to compress each row• Incremental or non-incremental path generation
• Fast First-Move Queries through Run-Length Encoding, Strasser, Harabor and Botea (2014)
• Complexity Results for Compressing Optimal Paths, Botea, Strasser and Harabor (2015)
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Contraction Hierarchies• Ben Strasser [KIT]
• Originally developed by [Geisberger et. al. 2008]• Wasn’t optimized for grids [Sturtevant and Geisberger, 2010]
• Later optimization for grids [Storandt, 2013]
• Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks, Robert Geisberger, Peter Sanders, Dominik Schultes and Daniel Delling, 2008
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
N-level Subgoals• Tansel Uras and Sven Koenig [USC]
• 3rd entry into GPPC• Builds a n-level hierarchy from the basic subgoal approach
• Basic subgoals are built up from visibility graphs
• Identifying Hierarchies for Fast Optimal Search, Uras and Koenig, 2014
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
JPS+• Steve Rabin [Digipen & Games Industry*]
• Independently invented JPS+• Based on Jump Point Search
• Improving Jump Point Search, Daniel Harabor and Alban Grastien, 2014
• Online Graph Pruning for Pathfinding On Grid Maps, Daniel Harabor and Alban Grastien, 2011
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
BLJPS• Jason Traish and James Tulip [Charles Sturt University]
• Boundary Lookup JPS• Alternate optimization similar to JPS+
• Also applied ideas to subgoals
• Optimization using Boundary Lookup Jump Point Search, Traish and Tulip, 2015
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Relaxed A*• http://www.iroboapp.org/• Doesn’t perform A* re-expansions & other optimizations• Also applied to subgoal search
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Results
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Non-DominatedApproaches
• RA*, RA* Subgoal• BLJPS, BLJPS2• N-level Subgoals• Contraction Hierarchies (CH)• Single-Row Compression (SRC) (2 variants)
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Speed vs Storage (2014)Entry Average (ms) Storage
RA* 282.995 0
BLJPS 14.453 20 MB
BLJPS2 7.444 47 MB
RA* Subgoal 1.688 264 MB
NSubgoal 0.773 293 MB
CH 0.362 2.4 GB
SRC-dfs 0.145 28 GB
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
![Page 63: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/63.jpg)
JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
![Page 65: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/65.jpg)
JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
![Page 66: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/66.jpg)
JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
![Page 67: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/67.jpg)
JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
![Page 68: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/68.jpg)
JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
![Page 69: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/69.jpg)
JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
![Page 71: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/71.jpg)
JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
![Page 73: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/73.jpg)
DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Contractions everywhere!• Describe majority of approaches as contraction:
• Contraction Hierarchies• DAO abstraction• Subgoal Graphs• Jump Point Search
36
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Graph Contraction• Remove a set S of states from a graph G• Optimal:
• Ensure that the shortest path between all states G \ S are not changed
• Add edges (shortcuts) to preserve shortest paths• Suboptimal:
• Ensure that completeness is not lost
37
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11 1
1
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4
![Page 77: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/77.jpg)
1
22
2 2
2
2
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22
2 2
1
2
2
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22
2 2
1
2
2
![Page 80: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/80.jpg)
22
2 2
1
2
2
![Page 81: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/81.jpg)
22
2 2
1
2
2
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22
2 2
1
2
2
![Page 83: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/83.jpg)
22
2 2
1
2
2
4
![Page 84: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/84.jpg)
1
22
2 2
2
2
![Page 85: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/85.jpg)
1
22
2 2
2
2
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Contraction Hierarchies• Optimal approach• Key idea is finding good orderings for contracting nodes from the graph
• Contract one node at a time• Add shortcut edges
43
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Traditional Abstraction/Refinement
• Find strongly connected components• Abstract them together into a single abstract state• (Holte et al, 1996), (Fernández, & González, 2002), (Botea et. at., 2004), (Sturtevant & Buro, 2005), (Sturtevant 2007)
• Downward refinement property• Approach discarded in road networks after optimal approaches discovered
44
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a
b
a b c
a
b
a
b
0 1
2 3
![Page 90: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/90.jpg)
JPS
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JPS
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JPS
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JPS
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JPS
![Page 95: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/95.jpg)
JPS
![Page 96: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/96.jpg)
JPS
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JPS
![Page 98: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/98.jpg)
JPS
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JPS
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JPS
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JPS
![Page 102: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/102.jpg)
JPS
![Page 103: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/103.jpg)
S
![Page 104: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/104.jpg)
S
![Page 105: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/105.jpg)
S
![Page 106: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/106.jpg)
S
![Page 107: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/107.jpg)
S
![Page 108: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/108.jpg)
S
![Page 109: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/109.jpg)
S
![Page 110: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/110.jpg)
S
![Page 111: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/111.jpg)
S
![Page 112: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/112.jpg)
S
![Page 113: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/113.jpg)
S
![Page 114: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/114.jpg)
Subgoals
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Subgoals
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Subgoals
![Page 117: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/117.jpg)
Direct H Reachable
Subgoals
![Page 118: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/118.jpg)
Direct H Reachable
Subgoals
![Page 119: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/119.jpg)
Direct H Reachable
Subgoals
![Page 120: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/120.jpg)
Direct H Reachable
Subgoals
![Page 121: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/121.jpg)
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Other contractions• Dead-end heuristic
• Yngvi Björnsson and Kári Halldórsson, 2006• Swamps
• Nir Pochter, Aviv Zohar, Jeffrey S. Rosenschein, Ariel Felner [2008 - 2010]
• Dead/redundant states• N.R. Sturtevant, V. Bulitko and Y. Bjornsson, 2010
• What is the correct way to contract a map?
55
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Highway DimensionHighway Dimension, Shortest Paths, and Provably Efficient Algorithms [Abraham et. al., 2010]
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Highway Dimension
r
Highway Dimension, Shortest Paths, and Provably Efficient Algorithms [Abraham et. al., 2010]
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Highway Dimension
r4r
Highway Dimension, Shortest Paths, and Provably Efficient Algorithms [Abraham et. al., 2010]
![Page 130: The Grid-Based Path Planning Competition](https://reader030.fdocuments.net/reader030/viewer/2022012021/61689886d394e9041f70f5db/html5/thumbnails/130.jpg)
Highway Dimension
r4r
Highway Dimension, Shortest Paths, and Provably Efficient Algorithms [Abraham et. al., 2010]
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Cross-Fertilization• Many road network ideas being used in grids• Didn’t originally know how to apply them properly
• Contraction Hierarchies on Grid Graphs • Storandt, 2013
• TRANSIT Routing on Video Game Maps• Antsfeld, Harabor, Kilby & Walsh, 2012
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Further use of contractions?• Where else could we apply contractions?
• Robotics?• 3D worlds?• Alternate representations? (polygons)
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
The Future• Have we reached the limits of our performance?• Where is there significant room for improvement?• Other future directions?
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
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JPS+ (Rabin)
CH
SRC-dfs
SRC-dfs-i
N-Level Subgoal
SUB Variants JPS+ Bucket (Rabin)
BLJPS+Sub
PPQ
PDH
Tree (13)Tree (12)
DAO1
Block A*
RA*
JPS (Harabor)
BLJPS
BLJPS2
JPS+ (Harabor)
Max
Tim
e pe
r Seg
men
t (m
s)
10−3
10−2
10−1
1
101
102
103
Storage (MB)1 101 102 103 104 105
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Is this the real problem?• Dynamic world
• Costs change, connectivity changes
• Cell costs
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Open Question• Are we building insight?
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Open Question• Are we building insight?
• The benchmarks are helping drive research
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Open Question• Are we building insight?
• The benchmarks are helping drive research• Work is leading to new theoretical understanding
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Open Question• Are we building insight?
• The benchmarks are helping drive research• Work is leading to new theoretical understanding
• Thanks to SoCS chairs for the chance to contribute to the understanding
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
One more thing!• New benchmark data
• Warframe video(?)• Example maps(?)
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Warframe - Digital Extremes
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
New repository coming• 3D voxel world• Challenging new path planning domain
• Thanks to Digital Extremes and Daniel Brewer!
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DANIEL FELIX RITCHIE SCHOOL OFENGINEERING & COMPUTER SCIENCE
Benchmarks, Grid-Based Path Planning, and Contractions
Thanks• Students/Collaborators
• Renee Jansen• Sally Li• Michael Buro• Vadim Bulitko• Robert Geisberger
• http://movingai.com/GPPC/
• Games Industry• BioWare• Digital Extremes
• Daniel Brewer• Troy Humphreys
• GPPC Participants• SoCS Organizers
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NINJAS&PLAY&FREE&AT&
WWW.WARFRAME.COM