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Lars ArgeGerth Stølting Brodal
Algorithms and Data Structures
Computer Science Day, Department of Computer Science, Aarhus University, May 31, 2013
May 232013
MADALGO – CTIC 6 : 3 May 23 2013
MortenCasperJakobJesperConstantinosDarius
Phd
Post
Doc
Lars(Professor)
Speciale
DanielJana Morten
Jørgen Jeppe
Jens
Steffen
Jakob
Mikkel
Yungwoo(PhD)
Zhewei(PostDoc)
Bryan(PhD)
Peyman(Adjunkt)
Gerth(Lektor)
Sarfraz
(PhD)
Else(Manager)
Allan(PostDoc)
Else’s rubber boots
Lars
Water
Lars’ house
Brabrand lake
Lars’ house
Lars’ house
Research
AlgorithmicsTheory
Practical
Commercial
Peyman
GerthLars
EcoInformaticsBioInformaticsCOWI, DES, EIVA, …
Terrain Research
3 2 47 5 87 1 9
3 2 47 5 87 1 9
3 2 47 5 87 1 9
3 2 47 5 87 1 9
Height matrix
Terrain model
Range Minimum Queries (1D)1 2 3 4 5 6 7 8
n9
0.3 0.1 3.5 2.4 0.7 5.2 1.6 3.7 4.2
RMQ(3,6) = 5
0.30.1
3.52.4
0.7
5.21.6
3.74.2
1
2
3
4
6
7
8
9
1 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 0 02L 1L 1R 2R 5L 4L 3L 3R 4R 5R 7L 6L 6R 7R 8L 8R 9L 9R
Cartesian tree [Vuillemin 1980]55
2n bit encoding
2n+o(n) bit encodingO(1) time queries
[Fischer, Heun 2011]
Range Minimum Queries (2D)
nm log(nm) bit encoding
1 2 3 4n5
1 0.3 0.1 3.5 2.4 0.72 5.2 1.6 0.6 4.2 8.7
m 3 1.4 3.8 6.5 4.1 0.2
1 2 3 4n5
1 0.3 0.1 3.5 2.4 0.72 5.2 1.6 0.6 4.2 8.7
m 3 1.4 3.8 6.5 4.1 0.2
1 2 3 4n5
1 0.3 0.1 3.5 2.4 0.72 5.2 1.6 0.6 4.2 8.7
m 3 1.4 3.8 6.5 4.1 0.2
RMQ(2,2,3,4) = (2,3)
1 2 3 4n5
1 3 1 9 8 52 13 7 4 12 15
m 3 6 10 14 11 2
Rank matrix
Lower bound: (nmlog m)[Brodal, Davoodi, Rao 2012]
Upper bound: O(nmlog m)[Brodal, Brodnik, Davoodi 2013]
Query time ?
Research
AlgorithmicsTheory
Practical
Commercial
Peyman
GerthLars
EcoInformaticsBioInformaticsCOWI, DES, EIVA, …
Lars ArgeGerth Stølting Brodal
Thank you