BRICS Research Activities Algorithms
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1 BRICS Research Activities Algorithms Gerth Stølting Brodal BRICS Retreat, Sandbjerg, October
2 Outline of Talk The Algorithms Group Courses Algorithm Events Expertise within BRICS Examples Algorithms for Evolutionary Trees Cache Oblivious Algorithms BRICS Retreat, Sandbjerg, October
3 The Algorithms Group Erik Meineche Schmidt Algorithms, Complexity Theory Sven Skyum Algorithms, Complexity Theory Peter Bro Miltersen Complexity Theory, Data Structures Gudmund Skovbjerg Frandsen Algebraic Algorithms, Dynamic Algorithms Christian Nørgaard Storm Pedersen Bioinformatics, String Algorithms Gerth Stølting Brodal Data Structures, External Memory PhD students Alex Rune Berg Graph Theory Jesper Makholm Byskov Algorithms for NP-hard problems Bolette Ammitzbøll Madsen Algorithms for NP-hard problems Bjarke Skjernaa Algorithms for NP-hard problems Kristoffer Arnsfelt Hansen Complexity Rolf Fagerberg Data structures, External Memory BRICS Retreat, Sandbjerg, October
4 Courses dprog (Introduction to Programming) Frandsen dads (Algorithms and Data Structures) Brodal, Schmidt dsøgopt (Searching and Optimization) Skyum, Miltersen Computer Architecture and Operating Systems Pedersen Computational Geometry Skyum Complexity Miltersen Randomized, Parallel and Dynamic Algorithms Frandsen Algorithms (ph.d. course) Brodal, Fagerberg External Memory Algorithms and Data Structures Algorithms for Web Indexing and Searching Algorithms in Bioinformatics Pedersen Genome Analysis BRICS Retreat, Sandbjerg, October
5 Algorithm Events Upcoming 18th IEEE Conference on Computational Complexity (June 2003, organizing chair Peter Bro Miltersen) Ongoing Alcom seminar Recent EEF Summer School on Massive Data Sets (June 2002) ALGO 2001 (August 2001) ESA th Annual European Symposium on Algorithms WAE th Workshop on Algorithm Engineering WABI st Workshop on Algorithms in BioInformatics BRICS Retreat, Sandbjerg, October
6 Algorithms and Complexity Future Technologies The ALCOM-FT project is a joint effort between eleven of the leading groups in algorithms research in Europe. The aim of the project is to discover new algorithmic concepts, identify key algorithmic problems in important applications, and contribute to the accelerated transfer of advanced algorithmic techniques into commercial systems. The project takes place from June 2000 to June ALCOM-FT (continuation of ALCOM, ALCOM-II, ALCOM-IT) BRICS is the coordinator of ALCOM-FT (Erik Meineche Schmidt, Rolf Fagerberg) 336 technical reports since July 2000 BRICS Retreat, Sandbjerg, October
7 BRICS Barcelona Cologne INRIA Rocquencourt Max-Planck-Institut für Informatik Paderborn Patras Rome La Sapienza Utrecht Warwick Cyprus Erik Meineche Schmidt Josep Díaz Michael Jünger Philippe Flajolet Kurt Mehlhorn Burkhard Monien Friedhelm Meyer auf der Heide Paul Spirakis Giorgio Ausiello Jan van Leeuwen Mike Paterson Marios Mavronicolas BRICS Retreat, Sandbjerg, October
8 Algorithm Expertise within BRICS Algorithms in general Complexity Data structures Dynamic algorithms External memory algorithms Algorithms in Bioinformatics Algorithm engineering / experimental algorithmics BRICS Retreat, Sandbjerg, October
9 Examples BRICS Retreat, Sandbjerg, October
10 Algorithms for Evolutionary Trees a c a b c d d b f e f e d b c b induced quartets a c a d Reconstruct evolutionary trees, e.g. from quartets Compare evolutionary trees, e.g. number of common quartets BRICS Retreat, Sandbjerg, October
11 The Classic RAM Model CPU R A M Add: O(1) Mult: O(1) Mem access: O(1) BRICS Retreat, Sandbjerg, October
12 The Classic RAM Model CPU R A M Add: O(1) Mult: O(1) Mem access: O(1) Real life CPU L1 C a c h e L2 C ac h e R A M Disk Bottleneck: transfer between two highest memory levels in use BRICS Retreat, Sandbjerg, October
13 The I/O Model I/O CPU m e M y ro External Memory N = problem size M = memory size B = I/O block size Aggarwal and Vitter 1988 One I/O moves B consecutive records from/to disk Cost: number of I/Os E.g., sorting requires O ( N B log M/B N B ) I/Os. BRICS Retreat, Sandbjerg, October
14 Cache-Oblivious Model Frigo, Leiserson, Prokop, Ramachandran, FOCS 99 Program in the RAM model Analyze in the I/O model (for arbitrary B and M). Advantages Optimal on arbitrary level optimal on all levels. B and M not hard-wired into algorithm. BRICS Retreat, Sandbjerg, October
15 Cache-Oblivious Results Scanning stack, queue, median finding,.... Sorting, matrix multiplication, FFT Frigo, Leiserson, Prokop, Ramachandran, FOCS 99 Cache oblivious search trees Prokop 99 Bender, Demaine, Farach-Colton, FOCS 00 Rahman, Cole, Raman, WAE 01 Bender, Duan, Iacono, Wu and Brodal, Fagerberg, Jacob, SODA 02 Priority queue and graph algorithms Arge, Bender, Demaine, Holland-Minkley, Munro, STOC 02 Brodal, Fagerberg, ISAAC 02 Computational geometry Scanning dynamic sets Bender, Cole, Raman, ICALP 02 Brodal, Fagerberg, ICALP 02 Bender, Cole, Demaine, Farach-Colton, ESA 02 BRICS Retreat, Sandbjerg, October
16 Double for-loop X, Y arrays of length n: X Y i j I/O complexity: n n B = n2 B BRICS Retreat, Sandbjerg, October
17 Double for-loop M X More I/O-efficient version: Y M I/O complexity: n M n M M B = n2 MB BRICS Retreat, Sandbjerg, October
18 Double for-loop Cache-oblivious version: n/2 n/2 X Y + recursion n/2 n/2 I/O complexity: Again n2 MB BRICS Retreat, Sandbjerg, October
19 Double for-loop Cache-oblivious version BRICS Retreat, Sandbjerg, October
20 Double for-loop Experiments time (seconds) plain cache-aware (L1) log 2 of array size (bytes) cache-aware (L2) cache-oblivious Sizes within RAM (element size 4 bytes) 366 MHz Pentium II, 128 MB RAM, 256 KB Cache, gcc -O3, Linux BRICS Retreat, Sandbjerg, October
21 Double for-loop Experiments time (seconds) log 2 of array size (bytes) plain cache-aware (L2) cache-aware (RAM) cache-oblivious Sizes exceeding RAM (element size 1 KB) 366 MHz Pentium II, 128 MB RAM, 256 KB Cache, gcc -O3, Linux BRICS Retreat, Sandbjerg, October
22 Cache-Oblivious Search Trees Recursive memory layout (van Emde Boas layout) Prokop 1999 h/2 A h B 1 B k h/2 A B 1 B k Binary tree Dynamization Searches use O(log B N) I/Os Bender, Demaine, Farach-Colton, FOCS 00 Rahman, Cole, Raman, WAE 01 Bender, Duan, Iacono, Wu, SODA 02 Brodal, Fagerberg, Jacob, SODA 02 BRICS Retreat, Sandbjerg, October
23 Cache-Oblivious Search Trees Search O(log B N) Range Reporting Updates ) O ( log B N + k B O ( log B N + log2 N B ) BRICS Retreat, Sandbjerg, October
24 Current Work... M B 2? BRICS Retreat, Sandbjerg, October
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