An efficient parallel algorithm for the row minima of a totally monotone matrix

Abstract

We give a parallel algorithm for the problem of computing the row minima of a totally monotone two-dimensional matrix. Whereas the previous best CREW-PRAM algorithm for this problem ran in O(log n log log n) time with O(n/ log log n) processors, our algorithm runs in O(log n) time with O(n) processors in the (weaker) EREW·PRAM model. Thus we simultaneously improve the time complexity without any deterioration in the time x processors produd, even using a weaker model of parallel computation. ·Dept. of Computer Science, Purdue University, Weat La£ayette, IN 47907. This author's research was supported by the Office of NavaJ Research under Contracts N00014·84-K-0502 and N00014-86-K-0689, the Air Force Office of Scientific Re~earch under Grant AFOSR-90-0107, Lhe National Science Foundation under Grant DCR-8451393, and the National Library of Medicine under Grant R01·LM05118. IDept. of Computer Science, Johns Hopkins University, Baltimore, MD 21218. This author's research was supported by the National Science Foundation under Grant CCR-8804284 and NSF/DARPA Grant CCR·890a092.