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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

?

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

S

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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