1. Holger Bast Benjamin Doerr Stefan Funke Joachim Giesen Kurt Mehlhorn Uli Meyer AG1: Ways of Working & Project Ideas MPI Retreat, Braunshausen, 12 th May 2006

2. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006 AG1: Snapshot from 2005 EXPERIM.APPLIED THEORY

3. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006 EXPERIM.APPLIED THEORY AG1: Typical Results 1/3

4. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006 Matrix Rounding Given an n x n matrix, round each entry x to one of ⌊ x ⌋ or ⌈ x ⌉, such that maximal sum of differences in a sub-rectangle is minimized Komlós, Gabor, Tusnády 1975: is there an O(1) upper bound? Beck 1981: lower bound of log n, upper bound of (log n) 4, later (log n) 3.5+ε Bohus 1990: upper bound of (log n) 3.5 Matoušek 1995: upper bound of (log n) 2.5 (log log n) 0.5 Srinivasan 1997: upper bound of (log n) 2.5 Relaxation: each entry may be rounded to one of ⌊ x ⌋ -1, ⌊ x ⌋, ⌈ x ⌉, ⌈ x ⌉ + 1 Doerr 2003: upper bound of log n [SODA + European Journal of Combinatorics] Doerr, Güntürk, Yılmaz 2006: upper bound of 2 [to be submitted] 9.73.61.5 2.14.73.9 1.43.78.3 1041 244 248 difference in sub-rectangle: | 0.3 + 0.4 - 0.1 - 0.7 | = 0.1 AG1: Typical Results 1/3

5. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006 EXPERIM.APPLIED THEORY AG1: Typical Results 1/3

6. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006 EXPERIM.APPLIED THEORY AG1: Typical Results 2/3

7. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006 Robust Computational Geometry Goal: evaluation of critical predicates exactly but still efficiently e.g., say whether a given point is on a given line, or to its left or to its right Sample results: Arrangement of Curved Objects Eigenwillig, Kettner, Mehlhorn, Schömer, … SCG'04 (cubic curves), SCG'05 (some quartic curves) ESA'05 (EXACUS library) Mathematics for predicate design Experiments to demonstrate efficiency compute convex hull AG1: Typical Results 2/3

8. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006 EXPERIM.APPLIED THEORY AG1: Typical Results 2/3

9. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006 EXPERIM.APPLIED THEORY AG1: Typical Results 3/3

10. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006 Autocompletion Search Engine Theory on central index data structure entropy(our new index) ≤ (1+ε)∙entropy(standard index) formulas for expected query processing time (under simplifying probablistic assumptions) Experiments on Terabyte Benchmark (25 million documents) standard index: 4.6 GB of space, up to 30 seconds per query our new index: 4.8 GB of space, never more than 50 milliseconds per query Usable Search Engine JavaScript, Ajax, Cookies, Debugging a Web Application, Apache, Socket Communication, Crawling, GUI, real data: äöüß, UTF, PS/PDF/DOC,... AG1: Typical Results 3/3 SIGIR 2006

11. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006 EXPERIM.APPLIED THEORY AG1: Typical Results 3/3

12. AG1 Ways of Working & Project Ideas – MPI Retreat, Braunshausen, 12 th May 2006

13. Project Ideas Goals cross departmental collaboration strong outside visibility external funding (DFG, VW-Stiftung?) work packages / responsibilities proposal within six months duration ~ two years spin off?