## Simulation of PRAM Models on Meshes (1994)

Venue: | Nordic Journal on Computing, 2(1):51 |

Citations: | 14 - 9 self |

### BibTeX

@ARTICLE{Leppänen94simulationof,

author = {Ville Leppänen and Martti Penttonen},

title = {Simulation of PRAM Models on Meshes},

journal = {Nordic Journal on Computing, 2(1):51},

year = {1994},

volume = {2},

pages = {51--69}

}

### OpenURL

### Abstract

We analyze the complexity of simulating a PRAM (parallel random access machine) on a mesh structured distributed memory machine. By utilizing suitable algorithms for randomized hashing, routing in a mesh, and sorting in a mesh, we prove that simulation of a PRAM on p N \Theta p N (or 3 p N \Theta 3 p N \Theta 3 p N ) mesh is possible with O( p N ) (respectively O( 3 p N )) delay with high probability and a relatively small constant. Furthermore, with more sophisticated simulations further speed-ups are achieved; experiments show delays as low as p N + o( p N ) (respectively 3 p N + o( 3 p N )) per N PRAM processors. These simulations compare quite favorably with PRAM simulations on butterfly and hypercube. 1 Introduction PRAM 1 (Parallel Random Access Machine) is an abstract model of computation. It consists of N processors, each of which may have some local memory and registers, and a global shared memory of size m. A step of a PRAM is often seen to consist of...