exact matching: topics
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1 Exc Mching
2 exc mching: pics exc mching serch pern P in ex T (P,T srings) Knuh Mrris Pr preprcessing pern P Ah Crsick pern f severl srings P = { P 1,, P r } Suffix Trees preprcessing ex T r severl exs dse
3 (A) preprcessing perns Knuh-Mrris-Pr Ah-Crsick
4 KMP exmple filure links (suffix = prefix) p: s umn m: s le hw deermine? hw use?
5 KMP cmpuing filure links filure link ~ new es mch (fer mismch) òr 0 k-1 k Flink[1] = 0; fr k frm 2 PLen d fil = Flink[k-1] while ( fil>0 nd P[fil] P[k-1] ) d fil = Flink[fil]; d Flink[k] = fil+1; d
6 prefixes vi filure links P r k Flink[k]=r P r P 1 P r-1 = P k-r+1 P k-1 mximl r<k ll such vlues r: r 4 r 3 r 2 r 1 k P 1 P r2-1 = P k-r2+1 P k-1 = P r1-r2+1 P r1-1 Flink[r 1 ]=r 2
7 her mehds Byer-Mre T = mrkkpmn P = schenveer sche wrk ckwrds Krp-Rin fingerprin fingerprin i-1 i i+n-1 i+n p 1 p n hsh-vlue i B n-1 + i+1 B n-2 + i+n-1 B 0 i+1 B n i+n-1 B 1 + i+n B 0
8 exc mching wih se f perns P = { P 1,, P r } ll ccurrences in ex T l lengh m lengh n AHO CORASICK generlizes KMP filure links lnges suffix h is prefix (perhps in nher sring) > n suwrds wihin P
9 keywrd ree - rie edges ~ leers e p e r r s y i c e n h c { p, pery, pery, science, schl } l y e leves ~ keywrds
10 filure links p h e h e r e { p,, heer, her } r p her p filure links in her rnches!
11 lgrihm: fllw he links exising new edge wih incming fllw links sring pren unil uging is fund
12 filure links p h e h e r e { p,, heer, her } r p her heer p redh firs (level-y-level)
13 filure links p e r h { p,, heer, her } h e r e r child r [single leer] shrcus
14 (B) preprcessing ex
15 rie vs. suffix ree sring+suffixes rie suffix ree
16 rie vs. ree Trie(T) = O( T ) 2 qudric d exmple: T = n n Trie(T) like DFA fr he suffixes f T minimize DFA direced cyclic wrd grph nly rnching ndes nd leves represened edges leled y susrings f T crrespndence f leves nd suffixes T leves, hence < T inernl ndes Tree(T) = O( T + size(edge lels)) liner
17 niygriy niygriy iygriy ygriy ygriy ygriy griy riy iy y y y niygriy griy 2 8 griy y iy y y griy griy griy
18 niygriy niygriy iygriy ygriy ygriy ygriy griy riy iy y y y niygriy 1-11 griy iy y griy 6-11 griy 6-11 y y 5-5 griy 6-11 griy implemenin: refer psiins
19 liner ime cnsrucin niygriy iygriy ygriy ygriy ygriy griy riy iy y y y Weiner (1973) lgrihm f he yer McCreigh (1976) n-line lgrihm (Ukknen 1992)
20 suffix rie fr suffix links nex syml = frm here lredy exiss
21 pplicin: full ex index T ps P ps P in T P is prefix f suffix f T P suree under P ~ lcins f P ps ps
22 exmple: find i in niygriy niygriy iygriy ygriy ygriy ygriy griy riy iy y y y niygriy griy 2 8 iy griy y griy y 6 y griy griy psiins
23 pplicin: lnges cmmn susring T P pples ple T ps ps P generlized suffix ree (mrk T nd T suffixes) ps ps
24 pplicin: cuning mifs niygriy iygriy ygriy ygriy ygriy griy riy iy y y y niygriy griy 2 8 iy y 2 griy 2 griy y 6 4 griy y griy
25 mif : repes in DNA s repred y Ukknen humn chrmsme 3 he firs ses 31 min cpu ime (8 prcessrs, 4 GB) humn genme: 3x10 9 ses suffix ree fr Humn Genme fesile
26 lnges repe? Occurrences : , r Lengh: 2559 gggcggcccggcgggcgccggccgggggcgccccccgcgcg ggcccggccccccccccccccccccccccgccccggggggccccccggccggcc gccccccggggcgcggggggccgcgggcgggggccgcccc ccccggcgcccggcgcgccgggggcccccccgccccgg gccgggggccgcgcggggccgcccgggcggcgcgcgcc gggcccggggggcgggcggcgcgcccgggcccccgccccgg gcgcgcccgccgcccccccccccgcccggccgcgcgccccg ggggggccgggggcccgggccgggggccggggcgcgc cggggcgccccgccccgggggggcgggggcggcggg gcccgcggggggccccccggggccgcccgggggccgcggcggcc ggcccgcggcggccgcggggcggccgcccgccgccgg ggccggccgggggggccggccccggggggg ggggggggggggggccgcgcccggcg ccgcccgcccgggccccccgcggcgggcgcgggggcgg ccggggccgcgccggcccgggccgccgcgggcggccggg ggcgggcggggccgcgcggcgggcggcggggccggccgcg gcccgggcgggcgggggggcgccccgggcgggcccc gccccccggcggcgcccggccccggcgggggcccgggg cccccccggggccggccggcggggggcccggcccggcg gggggcgggccggccggcgcgggccgcggggggcg gcgggggcgccgccgccgggcgccccccgcccgccccc cgccggcccggccgcccccgggggggggggggccccgcggccgcggg gcccggcccggggcgggggcggccggccccccc ggggcgggcggcggcccgccggcgggcgcggcg gcgggcggcgggccgccgccccgggggccccgcgggggcgg gcgcggcgggccggggcgccggccggggcccgggccg cggcggcggggcggcccgggg
27 en ccurrences? ggcgggccgccgcgcccggcggggcgg gcgggccggcccgcgcccgcccccgggccgccc ccgcccgcccccggcgggccggcgcccgccccg cccggcggggcggggcccggccgg gggccgcccgcccggccgcccgcccggcccccg gcgggcggcg Lengh: 277 Occurrences : , , , , , In he reversed cmplemen : , , ,
28 finlly suffix ree efficien (liner) srge, u cnsn ±40 lrge verhed suffix rry hs cnsn ±5 hence mre prcicl u hs is wn cmplicins nïve n lg(n) lgrihm n d
29 suffix rry niygriy iygriy ygriy ygriy ygriy griy riy iy y y y griy iy iygriy niygriy riy y ygriy y ygriy y ygriy lexicgrphic rder f he suffixes
30 surces Dn Gusfield Algrihms n Srings, Trees, nd Sequences Cmpuer Science nd Cmpuinl Bilgy liss mny pplicins fr suffix rees (nd exended implemenin deils) slides n suffix-rees sed n/cpied frm Esk Ukknen, Univ Helsinki (Erice Schl, 30 Oc 2005)
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