Parallel two dimensional witness computation

Richard Cole, Zvi Galil, Ramesh Hariharan, S. Muthukrishnan, Kunsoo Park

Abstract: An optimal parallel CRCW-PRAM algorithm to compute witnesses for all non-period vectors of an m1×m2 pattern is given. The algorithm takes O(loglogm)<math><mtext>O(</mtext><mtext>log</mtext><mspace xmlns="true" sp="0.12" width="2px" linebreak="nobreak" is="true"></mspace><mtext>log</mtext><mtext>m)</mtext></math> time and does O(m1×m2) work, where m=max{m1,m2}. This yields a work optimal algorithm for 2D pattern matching which takes O(loglogm)<math><mtext>O(</mtext><mtext>log</mtext><mspace xmlns="true" sp="0.12" width="2px" linebreak="nobreak" is="true"></mspace><mtext>log</mtext><mtext>m)</mtext></math> preprocessing time and O(1) text processing time.