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

Abstract— In this article, we propose a fully distributed algorithm for finding all primes in an 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, the 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 + √ n. 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 n∆N + √ n∆N , where ...

• Type: Conference
• Year: 2005
• Where: ISPDC
• Authors: Gabriel Paillard, Christian Antoine Louis Lavault, Felipe Maia Galvão França
• Keywords: Algorithm, ISPDC 2005, Multiple Edge Reversal, Prime Sieving Algorithms