Lars Arge Gerth Stølting Brodal Algorithms and Data Structures Computer Science Day, Department of...

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