A Distributed Prime Sieving Algorithm based on Scheduling by Multiple Edge Reversal

In this article, we propose a fully distributed algorithm for finding all primes in a given interval [2..n] (or (L, R), more generally), based on the SMER - scheduling by multiple edge reversal - multigraph dynamics. Given a multigraph M of arbitrary topology, having N nodes, an SMER-driven system is defined by the number of directed edges (arcs) between any two nodes of M and by the global period length of all "arc reversals" in M. In the domain of prime numbers generation, such a graph method shows quite elegant, and it also yields a totally new kind of distributed prime sieving algorithms of an entirely original design. The maximum number of steps required by the algorithm is at most n + radicn. Although far beyond the O(n/log log n) steps required by the improved sequential "wheel sieve" algorithms, our SMER-based algorithm is fully distributed and of linear (step) complexity. The message complexity of the algorithm is at most nDelta
_N
+ radicnDelta
_N
, where Delta
_N
denotes the maximum "multidegree" of the arbitrary multigraph M, and the space required per process is linear