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

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Presentation on theme: "Lars Arge Gerth Stølting Brodal Algorithms and Data Structures Computer Science Day, Department of Computer Science, Aarhus University, May 31, 2013."— Presentation transcript:

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

2 May

3 MADALGO – CTIC 6 : 3 May 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

7

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

9 Terrain Research Height matrix Terrain model

10 Range Minimum Queries (1D) n9n RMQ(3,6) = L2L 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 n5n m n5n m n5n m RMQ(2,2,3,4) = (2,3) 1234 n5n m 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


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