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1 Indxd Sarch Tr (Tri) Fawzi Emad Chau-Wn Tsng Dpartmnt of Computr Scinc Univrsity of Maryand, Cog Park Indxd Sarch Tr (Tri) Spcia cas of tr Appicab whn Ky C can b dcomposd into a squnc of subkys C 1, C 2, C n Rdundancy xists btwn subkys Approach Stor subky at ach nod Path through tri yids fu ky Examp Huffman tr C 3 C 2 C 1 C 4 C 3 1

2 Tris Usfu for sarching strings String dcomposs into squnc of ttrs Examp ART A R T Can b vry fast Lss ovrhad than hashing May rduc mmory Expoiting rdundancy May rquir mor mmory Expicity storing substrings E R A T ART S Typs of Tris Standard Sing charactr pr nod Comprssd Eiminating chains of nods Compact Stors indics into origina string(s) Suffix Stors a suffixs of string 2

3 Approach Standard Tris Each nod (xcpt root) is abd with a charactr Chidrn of nod ar ordrd (aphabticay) Paths from root to avs yid a input strings Tri for Mors Cod Standard Tri Examp For strings { a, an, and, any, at } 3

4 For strings Standard Tri Examp { bar, b, bid, bu, buy, s, stock, stop } b s i u t a d y o r c p k Standard Tris Nod structur Vau btwn 1 m Rfrnc to m chidrn Array or inkd ist Examp Cass Nod { Lttr vau; // Lttr V = { V 1, V 2, V m } Nod chid[ m ]; } 4

5 Efficincy Standard Tris Uss O(n) spac Supports sarch / insrt / dt in O(d m) tim For n d m tota siz of strings indxd by tri ngth of th paramtr string siz of th aphabt Word Matching Tri Insrt words into tri Each af stors occurrncs of word in th txt s a b a r? s s t o c k! s a b u? b u y s t o c k! b i d s t o c k! b i d s t o c k! h a r t h b? s t o p! b h s i u t a r 6 78 d 47, y 36 a r 69 0, c k o p 84 17, 40, 51, 62 5

6 Obsrvation Comprssd Tri Intrna nod v of T is rdundant if v has on chid and is not th root Approach A chain of rdundant nods can b comprssd Rpac chain with sing nod Incud concatnation of abs from chain Rsut Intrna nods hav at ast 2 chidrn Som nods hav mutip charactrs Comprssd Tri Examp b s id u to ar y ck p b s i u t a d y o r c p k 6

7 Compact Tris Compact rprsntation of a comprssd tri Approach For an array of strings S = S[0], S[s-1] Stor rangs of indics at ach nod Instad of substring Rprsnt as a tript of intgrs (i, j, k) Such that X = s[i][j..k] Examp: S[0] = abcd, (0,1,2) = bc Proprtis Uss O(s) spac, whr s = # of strings in th array Srvs as an auxiiary indx structur Compact Rprsntation Examp S[0] = S[1] = S[2] = S[3] = s b a r s s t o c k S[4] = S[5] = S[6] = S[7] = b u b u y b i d S[8] = S[9] = h a r b s t o p 1, 0, 0 7, 0, 3 0, 0, 0 1, 1, 1 6, 1, 2 4, 1, 1 0, 1, 1 3, 1, 2 1, 2, 3 8, 2, 3 4, 2, 3 5, 2, 2 0, 2, 2 2, 2, 3 3, 3, 4 9, 3, 3 7

8 Suffix Tri Comprssd tri of a suffixs of txt Examp: IPDPS Suffixs IPDPS PDPS DPS PS S Usfu for finding pattrn in any part of txt Occurrnc prfix of som suffix Examp: find PDP in IPDPS S P D I P P D D P P S S S S Suffix Tri Proprtis For String X with ngth n Aphabt of siz m Pattrn P with ngth d Uss O(n) spac Can b constructd in O(n) tim Find pattrn P in X in O(d m) tim Proportiona to ngth of pattrn, not txt 8

9 Suffix Tri Examp m i n i m i z i mi nimiz z miz nimiz z nimiz z 7, 7 1, 1 0, 1 2, 7 6, 7 4, 7 2, 7 6, 7 2, 7 6, 7 Tris and Wb Sarch Engins Sarch ngin indx Coction of a sarchab words Stord in comprssd tri Each af of tri Associatd with a word List of pags (URLs) containing that word Cad occurrnc ist Tri is kpt in mmory (fast) Occurrnc ists kpt in xtrna mmory Rankd by rvanc 9

10 DNA Computationa Bioogy Squnc of 4 diffrnt nucotids (ATCG) Portions of DNA squnc produc protins (gns) Gnom Mastr DNA squnc for organism For Human 46 chromosoms 3 biion nucotids 10

11 Tris and Computationa Bioogy ESTs Fragmnts of xprssd DNA Indicator for gns (& ocation) 5.5 miion squncs at NIH ESTmappr Buid suffix tri of gnom 8 hours, 60 Gbyts Sarch for ESTs in suffix tri 11 hours w/ 8 procssor Sun Sarch gnom w/ BLAST 5 + yars (prdictd) Gnom Suffix tr Mapping ESTs Gn 11