Large Scale Peer to Peer Performance Evaluations,
with Gauss-Jordan Method as an Example

Serge G. Petiton, and Lamine Aouad

Laboratoire d'Informatique Fondamentale de Lille
Universite des Sciences et Technologies de Lille
Cite Scientifique, M3
59655 Villeneuve d'Ascq, FRANCE

{petiton,aouad}@lifl.fr

Abstract. This paper presents a large scale block-based Gauss-Jordan
algorithm to invert very large dense matrices. This inversion proposes
to exploit a peer-to-peer platform. We assume that we access to a
acheduler that propose strategies allowing "owner computes" and data
migration anticipation heuristics. We present performance theoretical
evaluation results showing that an efficiency of 30% is possible to
invert a very large matrix on a platform where peers are heterogeneous
and interconnected by a 64 Mbits's network and with a sufficient
number of computers. If we use a fast internet, this simulation shows
that efficiency drop to 5%. Nevertheless, we discuss that, in this
case, the classical evaluation model is not well-adopted to this peer
to peer computing paradigm for large scale sientific computing with
heterogeneous computers.