e
i
r
Lau ing
n
e
D
Parallel Knu
th Morris Prat
t String Matc
hing CSE 633-­‐ Fa
l
l 2011 Outline ­ String Matching §  Knuth-­‐Morris-­‐Pratt Algorithm §  How to improve with parallelization ­ Experimental Set up §  Data Description §  Hardware SpeciGications ­ Results ­ Analysis ­ Future Work String Matching ­ Goal: Find occurrences of a pattern P of length m in a string S of length n (m < n) ­ Applications: §  Text Processing §  DNA & Protein sequence matching §  Anti-­‐Virus & Intrusion Detection §  Database Query Knuth-­‐Morris-­‐Pratt ­ The preGix function π[q] §  Encapsulates how the pattern matches against shifts of itself §  When there is a mismatch, the preGix function tells you how far to shift the pattern q 1 2 3 4 5 6 7 P[q] A B A B A C A Π[q] 0 0 1 2 3 0 1 §  Mismatch: P[q+1] != S[i] -­‐> q = π[q] In Parallel ­ Open MP on Shared Memory Machine ­ Matching multiple patterns on same text ­ If p = number of patterns, c = number of cores, S = input string ­ Find match faster by: §  Distribute p/c patterns to each core §  Distribute S to each core §  Projected speed up approximately c times Architecture Master Reads S from text And sends to each thread Run KMPMatch on S with PTHId Run KMPMatch on S with PTHId Run KMPMatch on S with PTHId Record Results in Struct Record Results in Struct Record Results in Struct Master can analyze results from Structs Experimental Set up -­‐ Data ­ Input Text §  100,000 lines each 256 characters §  Random 1 and 0 ­ Pattern §  Each permutation in order (ie binary counting) §  4 ‘bit’ through 13 ‘bit’ •  1, 2, and 3 ‘bit’ seemed too trivial §  Initial trials were Gixed on the 6 ‘bit’ pattern §  Time is average over 3 trials Experimental Set up -­‐ Hardware ­ 12 Core Machine §
§
2.4 GHz 48GB Memory ­ 32 Core Machine §  2.13GHz – INTEL §  2.2GHz – AMD §  256GB Memory ­ Initial tests varied threads from 1-­‐64 1 node: 32 cores 6 character pattern 50 45 40 35 30 25 20 15 10 5 0 0 5 10 15 20 25 Number of Threads 30 35 Processing time in Seconds Processing Time in Seconds Initial Results 1 node: 12 cores 6 character Pattern 16 14 12 10 8 6 4 2 0 0 2 4 6 8 10 Number of Threads §  RAM Time 32 Cores: 16.176 seconds §  Best Time 32 Cores: 13 threads – 3.575 seconds §  Deviation from 8-­‐21 threads is 0.1575 seconds §  RAM Time 12 Cores: 14.626 seconds §  Best Time 12 Cores: 12 threads – 2.384 seconds 12 14 Overall Results for 6 Character Pattern 1 through 64 threads 90 Time in Seconds 80 70 60 32 Core 50 40 12 Core 30 20 10 0 0 10 20 30 40 Number of Threads 50 60 70 Speedup Speedup On 32 Core Node Speedup on 12 Core Node 7 5 Speedup Factor Speedup Factor 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 6 5 4 3 2 1 0 0 5 10 15 20 25 Number of Threads Best Speedup 4.52x 30 35 0 2 4 6 8 10 Number of Threads Best Speedup 6.13x 12 14 How problem Size effects time 2500 Time in Seconds 2000 1500 RAM 1000 12 Threads 500 0 0 1000 2000 3000 4000 5000 6000 7000 Number of Patterns 8000 9000 Speedup 9 8 Speedup Factor 7 6 5 4 3 2 1 0 0 1000 2000 3000 4000 5000 6000 Number of Patterns 7000 8000 9000 Summary of Results §  Parallel good until number of threads exceeds number of cores §  14 ‘bit’, 16k patterns would not run on 12 core machine §  Max speedup on 12 core machine 6.13x not 12x §  Max speedup on 32 core machine even worse 4.52x not 32x! Future Work ­ Only compute preGix function one time for a pattern ­ Write results to a Gile rather than into a struct §  Memory issues with size of struct per pattern limited the length of pattern §  Writing to a Gile solves this issue ­ Examine load balancing directives References Fast Pattern Matching in Strings Donald E. Knuth, James H. Morris, Jr., and Vaughan R. Pratt, SIAM J. Comput. 6, 323 (1977), DOI:10.1137/0206024 Cormen, Thomas H., Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. "32 String Matching." Introduction to Algorithms. Cambridge, MA: MIT, 2009. 1002-­‐006. Print.