1. Lars Arge Gerth Stølting Brodal Algorithms and Data Structures Computer Science Day, Department of Computer Science, Aarhus University, May 31, 2013

2. May 23 2013

3. MADALGO – CTIC 6 : 3 May 23 2013 MortenCasperJakobJesper Constantinos Darius Phd PostDoc Lars (Professor) Speciale DanielJanaMorten Jørgen Jeppe Jens Steffen Jakob Mikkel Yungwoo (PhD) Zhewei (PostDoc) Bryan (PhD) Peyman (Adjunkt) Gerth (Lektor) Sarfraz (PhD) Else (Manager) Allan (PostDoc)

4. Else’s rubber boots Lars Water

5. Lars’ house Brabrand lake

6. Lars’ house

8. Research Algorithmics Theory Practical Commercial Peyman Gerth Lars EcoInformatics BioInformatics COWI, DES, EIVA, …

9. Terrain Research 324 758 719 324 758 719 324 758 719 324 758 719 Height matrix Terrain model

10. Range Minimum Queries (1D) 12345678 n9n9 0.30.13.52.40.75.21.63.74.2 RMQ(3,6) = 5 0.3 0.1 3.5 2.4 0.7 5.2 1.6 3.7 4.2 1 2 3 4 6 7 8 9 100111000110010100 2L2L 1L1L 1R1R 2R2R 5L5L 4L4L 3L3L 3R3R 4R4R 5R5R 7L7L 6L6L 6R6R 7R7R 8L8L 8R8R 9L9L 9R9R Cartesian tree [Vuillemin 1980] 55 2n bit encoding 2n+o(n) bit encoding O(1) time queries [Fischer, Heun 2011]

11. Range Minimum Queries (2D) nm   log(nm)  bit encoding 1234 n5n5 1 0.30.13.52.40.7 2 5.21.60.64.28.7 m 3 1.43.86.54.10.2 1234 n5n5 1 0.30.13.52.40.7 2 5.21.60.64.28.7 m 3 1.43.86.54.10.2 1234 n5n5 1 0.30.13.52.40.7 2 5.21.60.64.28.7 m 3 1.43.86.54.10.2 RMQ(2,2,3,4) = (2,3) 1234 n5n5 1 31985 2 13741215 m 3 61014112 Rank matrix Lower bound:  (nm  log m) [Brodal, Davoodi, Rao 2012] Upper bound: O(nm  log m) [Brodal, Brodnik, Davoodi 2013] Query time ?

12. Research Algorithmics Theory Practical Commercial Peyman Gerth Lars EcoInformatics BioInformatics COWI, DES, EIVA, …

13. Lars Arge Gerth Stølting Brodal Thank you