Abstract

. We consider three paradigms of computation where the benefits of a parallel solution are greater than usual. Paradigm 1 works on a time-varying input data set, whose size increases with time. In paradigm 2 the data set is fixed, but the processors may fail at any time with a given constant probability. In paradigm 3, the execution of a single operation may require more than one processor, for security or reliability reasons. We discuss the organization of PRAM algorithms for these paradigms, and prove new bounds on parallel speed-up. 1 Introduction The theory of parallel algorithms has a well known body, developed on the PRAM model [5]. Some folklore principles are at the base of this theory, in particular the ones that express upper and lower bounds on the processing time. Let \Pi be a problem of size N , and let T s (N) be the time required by the best known sequential algorithm A s to solve \Pi . Any parallel algorithm A p that solves \Pi with a number P of PRAM processors...

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