Algeng Workshop Google Routing
Transcript of Algeng Workshop Google Routing
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Algorithm Engineering for Large Graphs
Fast Route Planning
Veit Batz, Robert Geisberger , Dennis Luxen,Peter Sanders, Christian Vetter
Universitt Karlsruhe (TH)
Zuerich, September 2, 2008
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Route Planning
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Goals: exact shortest (i.e. fastest) paths in large road networks
fast queries (point-to-point, many-to-many)
fast preprocessing
low space consumption
fast update operations
Applications: route planning systems in the internet, car navigation systems,
ride sharing, trafc simulation, logistics optimisation
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Contraction Hierarchies[WEA 08]
order nodes by importance, V = {1 , 2 , . . . , n}
contract nodes in this order, node v is contracted by
foreach pair (u , v) and (v, w) of edges doif u , v, w is a unique shortest path then
add shortcut (u , w) with weight w( u , v, w )
query relaxes only edges
to more important nodes
valid due to shortcuts
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Contraction Hierarchies
foundation for our other methods
conceptually very simple
handles dynamic scenarios
Static scenario:
7.5 min preprocessing
0.21 ms to determine the path length
0.56 ms to determine a complete path description
little space consumption ( 23 bytes/node )
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Transit-Node Routing
[DIMACS Challenge 06, ALENEX 07, Science 07]
joint work with H. Bast, S. Funke, D. Matijevic
very fast queries
(down to 1.7 s, 3 000000 times faster than D IJKSTRA )
winner of the 9th DIMACS Implementation Challenge
more preprocessing time ( 2:37h ) and space ( 263 bytes/node ) needed
s t SciAm50 Award
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Mobile Contraction Hierarchies[ESA 08]
preprocess data on a personal computer
highly compressed blocked graph representation 8 bytes/node
compact route reconstruction data structure + 8 bytes/node
experiments on a Nokia N800 at 400 MHz
cold query with empty block cache 56ms
compute complete path 73ms
recomputation , e.g. if driver took the wrong exit 14ms
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Many-to-Many Shortest Paths
joint work with S. Knopp, F. Schulz, D. Wagner[ALENEX 07]
efcient many-to-many variant of
hierarchical bidirectional algorithms
10 000 10 000 table in 10s
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Ride Sharing
Current approaches:
match only ride offers with identical start/destination (perfect t)
sometimes radial search around start/destination
Our approach:
driver picks passenger up and gives him a ride to his destination
nd the driver with the minimal detour (reasonable t)
Efcient algorithm:
adaption of the many-to-many algorithm
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Dynamic Scenarios
change entire cost function
(e.g., use different speed prole)
change a few edge weights
(e.g., due to a trafc jam)
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Summary
static routing in road networks is easy
applications that require massive amount or routing
instantaneous mobile routing
techniques for advanced models
updating a few edge weights is OK
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Current / Future Work
Time-dependent edge weights
challenge: backward search impossible (?)
Multiple objective functions and restrictions (bridge height,. . . )
Multicriteria optimization (cost, time,. . . )
Integrate individual and public transportation
Other objectives for time-dependent travel
Routing driven trafc simulation