Computer Science Day 2013, May 31 12.15-13.00Distinguished Lecture: Andy Yao, Tsinghua University 13.15-13.30 Welcome and the 'Lecturer of the Year' award.

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1 Computer Science Day 2013, May 31 12.15-13.00Distinguished Lecture: Andy Yao, Tsinghua University 13.15-13.30 Welcome and the 'Lecturer of the Year' award 13.30-14.30 Data-Intensive Systems (Ira Assent) Computer Graphics and Image Processing (Toshiya Hachisuka) Bioinformatics (Søren Besenbacher) Use, Design and Innovation (Morten Kyng) Ubiquitous Computing and Interaction (Kaj Grønbæk) 14.30-14.45 Pause 14.45-15.45 Mathematical Computer Science (Peter Bro Miltersen) Cryptography and Security (Claudio Orlandi) Semantics and Logic (Lars Birkedal) Programming Languages (Anders Møller) Algorithms and Data Structures (Lars Arge) 15.45-Regnecentralen’s 1 year birthday party Large Auditorium, Incuba Science Park – Katrinebjerg http://cs.au.dk/csd2013

2 Algoritmer og Datastrukturer 2 Gerth Stølting Brodal Suffiks træer [GT, kapitel 9.2], Suffiks arrays [Smyth, kapitel 5.3.2]

3 Trier (text retrieval) bear bell bid bull buy sell stock stop Fredkin 1960

4 Præfiks-fri ? kan kat katrine kan$ kat$ katrine$ k a r i n n t e k a t r i n e n $ $ $

5 OrdPosition(er) a bear bell bid bull buy hear see sell stock stop the 4,28 6 78 47,58 30 36 69 0,24 12 17,40,51,62 84 74 Inverteret fil Søgning i Streng Trie

6 Komprimeret Trie Ukomprimeret trie

7 Komprimeret Trie over Ordbog (i,j,k) er delstrengen S[i][j..k]

8 Suffiks Træer Suffix træ = komprimeret trie over suffixer Plads O(n) Kan konstrueres i O(n) tid (for konstant størrelse alfabet) Weiner 1973

9 X

10 Suffiks Træ over to Strenge ABAB$ 0 BABA$ 1 wikipedia.org streng 1 : position 3 $01 længste strenge der forekommer i begge input strenge

11 Suffiks Array 1 2 3 4 5 6 7 8 tekst = a b a a b a a b Suffikser 1 a b a a b a a b 2 b a a b a a b 3 a a b a a b 4 a b a a b 5 b a a b 6 a a b 7 a b 8 b Sorterede suffikser 6 a a b 3 a a b a a b 7 a b 4 a b a a b 1 a b a a b a a b 8 b 5 b a a b 2 b a a b a a b 63741852 Suffix array σ

12 Algorithm SANaïve [Smyth, s.151] 0n+1 R-1

13 Algorithm SASimple [Smyth, s.151] 0n+1 R-1

14 SAComplex (P L ≥ P R ) P LM < P L :R←M, P R ←P LM P LM > P L :L←M P LM = P L : Start sammenligning på position P LM +1 Lad p være første forskellige position: u[p] < σ[M][p] : R←M, P R ←p-1 u[p] > σ[M][p] : L←M, P L ←p-1 præberegnet

15 Binært træ over intervaller Mihai Pătraşcu

16 Søgninger i et Suffiks Array n = tekst længde, m = mønster længde, k = antal forekomster