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8/12/2019 Flexible Route Planning With Contraction Hierarchies
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1 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
Institute for Theoretical Computer Science, Algorithmics II
Flexible Route Planning with ContractionHierarchiesRobert Geisberger,Moritz Kobitzschand Peter Sanders {geisberger,kobitzsch,sanders}@kit.edu
KIT University of the State of Baden-Wrttemberg and
National Large-scale Research Center of the Helmholtz Association www.kit.edu
8/12/2019 Flexible Route Planning With Contraction Hierarchies
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Motivation
2 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
route planningbecomesubiquitous
route planning servicese. g. Google Maps
wide spread generates widevariety of interests
multiple optimization criterias
possible (e.g. (time|cost) )
a
b c
d e
f(3|6)
(1|2)
(1|1)
(1|2)
(1|2)
(2|1)(3|0)
(3|1)
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Motivation
2 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
route planningbecomesubiquitous
route planning servicese. g. Google Maps
wide spread generates widevariety of interests
multiple optimization criterias
possible (e.g. (time|cost) )
a
b c
d e
f(3|6)
(1|2)
(1|1)
(1|2)
(1|2)
(2|1)(3|0)
(3|1)
a
f(3|6)
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Motivation
2 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
route planningbecomesubiquitous
route planning servicese. g. Google Maps
wide spread generates widevariety of interests
multiple optimization criterias
possible (e.g. (time|cost) )
a
b c
d e
f(3|6)
(1|2)
(1|1)
(1|2)
(1|2)
(2|1)(3|0)
(3|1)
a
f(3|6)
a
f(4|4)
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Motivation
2 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
route planningbecomesubiquitous
route planning servicese. g. Google Maps
wide spread generates widevariety of interests
multiple optimization criterias
possible (e.g. (time|cost) )
a
b c
d e
f(3|6)
(1|2)
(1|1)
(1|2)
(1|2)
(2|1)(3|0)
(3|1)
a
f(3|6)
a
f(4|4)
a
f
(7|2)
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Just imagine...
3 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
8/12/2019 Flexible Route Planning With Contraction Hierarchies
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Pareto Optimality
4 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
find allnon dominated routes
AdominatesB ifA is better orequal toBin every weight term
may result in an exponentialnumber of routes
heuristics necessaryto gain
practical algorithms
a
b c
d e
f
(1|2)
(1|1)
(1|2)
(1|2)
(3|0)
(3|1)
a
f(3|6)
(7|2)
(2|1)
(4|4)
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Pareto Optimality
4 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
find allnon dominated routes
AdominatesB ifA is better orequal toBin every weight term
may result in an exponentialnumber of routes
heuristics necessaryto gain
practical algorithms
a
b c
d e
f
(1|2)
(1|1)
(1|2)
(1|2)
(3|0)
(3|1)
a
f(3|6)
(7|2)
(2|3)
(4|6)
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Parameterized Optimality
5 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
linear combinationof weightterms
(t|c) t+p c
preprocessingconsidersallpossibleparameter values
queryforfixedparametersingle criteria techniques
parameter range allows to
selectmaximal impactof weightterms
p=0
a
b c
d e
f
(1|2)
(1|1)
(1|2)
(1|2)
(2|1)(3|0)
(3|1)
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Parameterized Optimality
5 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
linear combinationof weightterms
(t|c) t+p c
preprocessingconsidersallpossibleparameter values
queryforfixedparametersingle criteria techniques
parameter range allows to
selectmaximal impactof weightterms
p=0
0
1 1
2 4
3p=0 (3|6)
(1|2) 1
(1|1) 1
(1|2) 1
(1|2) 1
(2|1) 2(3|0) 3
(3|1) 3
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Parameterized Optimality
5 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
linear combinationof weightterms
(t|c) t+p c
preprocessingconsidersallpossibleparameter values
queryforfixedparametersingle criteria techniques
parameter range allows to
selectmaximal impactof weightterms
p=0
0
3 2
5 5
8p=1 (4|4)
(1|2) 3
(1|1) 2
(1|2) 3
(1|2) 3
(2|1) 3(3|0) 3
(3|1) 4
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Parameterized Optimality
5 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
linear combinationof weightterms
(t|c) t+p c
preprocessingconsidersallpossibleparameter values
queryforfixedparametersingle criteria techniques
parameter range allows to
selectmaximal impactof weightterms
p=0
0
5 3
7 6
11p=2 (7|2)
(1|2) 5
(1|1) 3
(1|2) 5
(1|2) 5
(2|1) 4(3|0) 3
(3|1) 5
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Parameterized Weight Functions
6 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
thedistance functiond(a, f)for two nodesa, f isconcave
monotone due to positive weight terms
a
b c
d e
f
(1|2)
(1|1)
(1|2)
(1|2)
(2|1)(3|0)
(3|1)
(3|6)
(4|4)
a
f (7|2)
p
d(a, f, p)
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Contraction Hierarchy Routing
7 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
order nodes by importance{v1,. . ., vn}
contractin thisorder
preserve original distancesby addingshortcuts
necessity of shortcutsdecided bywitness paths
query only relaxes edges tomore important nodes
a b c d
a
b
c
d
1 2 1
1
2
1
3
node
order
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Contraction Hierarchy Routing
7 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
order nodes by importance{v1,. . ., vn}
contractin thisorder
preserve original distancesby addingshortcuts
necessity of shortcutsdecided bywitness paths
query only relaxes edges tomore important nodes
a b c d
a
b
c
d
1 2 1
1
2
1
3
node
order
a d
a
d
b c
c
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Flexible Contraction Hierarchies
8 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
shortcuts in flexible scenario ifp :(a, b, c)is the only shortestpath
necessity of shortcuts only oncontinuous intervals storenecessity intervalin edges
necessity interval onaveragedeductable fromtwo single criteria
Dijkstra queriesquery uses only necessary edges
a c
d
(3|1) (3|1)
b
(2|4
) (2|4
)
p
d(a, c, p)
1/3 .
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Flexible Contraction Hierarchies
8 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
shortcuts in flexible scenario ifp :(a, b, c)is the only shortestpath
necessity of shortcuts only oncontinuous intervals storenecessity intervalin edges
necessity interval onaveragedeductable fromtwo single criteria
Dijkstra queriesquery uses only necessary edges
a c
d
(3|1) (3|1)
(4|8)b [0,1/3]
p
d(a, c, p)
1/3 .
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Flexible Contraction Hierarchies
9 Robert Geisberger, Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
single node order not practicalfor wide parameter range
a lot of shortcuts for all
parameter valuessplit parameter intervalwithheuristics
repeat as necessary
bucketsto supportfast
scanningof necessary edges
level
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Core-ALT for flex-CH
10 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
core based approach to
speed uppreprocessing(uncontracted core)
speed upquery(contractedcore)
usesALT algorithmon |k|topmostnodes
adaptable to flexible
scenario withlinearinterpolation
p
d(a, f, p)
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Profile Queries
11 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
findall possible paths
profile query withmaximal3 #paths 2queries
approximation: recursiononly if improvement largermore than(1 + )possible
p
d(a, f, p)
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Profile Queries
11 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
findall possible paths
profile query withmaximal3 #paths 2queries
approximation: recursiononly if improvement largermore than(1 + )possible
p
d(a, f, p)
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Profile Queries
11 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies
Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
findall possible paths
profile query withmaximal3 #paths 2queries
approximation: recursiononly if improvement largermore than(1 + )possible
p
d(a, f, p)
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Profile Queries
11 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction HierarchiesFaculty for Computer Science
Institute for Theoretical Computer Science, Algorithmics II
findall possible paths
profile query withmaximal3 #paths 2queries
approximation: recursiononly if improvement largermore than(1 + )possible
p
d(a, f, p)
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Experimental results
12 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction HierarchiesFaculty for Computer Science
Institute for Theoretical Computer Science, Algorithmics II
Table:Preprocessing and query performance for 64 landmarks on the Germanroad network, average over 10 000 queries. (4 692 751 nodes and 10 806 191directed edges)
core preproc space query speedup[hh:mm] [B/node] [ms]
- - 60 2 037.52 10 1 :54 159 2.90 698
uncontracted 5 000 1 :08 167 2.58 789
contracted 10 000 2 :07 183 0.63 3 234
E i l l
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Experimental results
13 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
0 0.125 0.25 0.5 1 2 4 8 16 32
0
10
20
30
40
50
60
epsilon (%)
# found pathsquery time [ms]
C i t SHARC
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Comparison to SHARC
14 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
Table:Approximated profile search on Western Europe
preproc # timealgorithm paths [ms]
flexCH 5 :15 0.00 12.5 21.9flexCH 5 :15 0.01 5.7 6.2
Pareto-SHARC 7 :12 (no guarantee) 5.3 35.4
C l i
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Conclusion
15 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
exact flexiblerouting for server scenarios
comparableeven tosingle criteriaspeedupscircumventsproblems of Pareto-optimality
scales wellthrough parameter splitting
Th k Y
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Thank You
16 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
Thank you for your attention.
Questions
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Questions
17 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
Questions?
Future Work
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Future Work
18 Robert Geisberger,Moritz Kobitzschand Peter Sanders:Flexible Route Planning with Contraction Hierarchies Faculty for Computer ScienceInstitute for Theoretical Computer Science, Algorithmics II
mobile implementation
applyparallelizationtechniquesmore than two weight terms (?)