In this paper we will present new adaptive routing algorithms for faulty processor arrays. Past research has shown that packet switched based communication performance in mesh connected networks is significantly degraded by the presence of faulty processors. Nondeterministic routing algorithms have been developed based on transport modeling of packet flow in disordered arrays. By utilizing nondeterministic routing strategies, based on biased random walkers, we can implement deadlock free routing, at the expense of not following the shortest path. These algorithms will be shown to be capable of increasing network bandwidth in the presence of faulty processors and interconnects. These algorithms offer an alternative to conventional adaptive routing techniques by utilizing a computationally simple algorithm based on local (nearest neighbor) information. Although we concentrate our efforts on 2 dimensional processor arrays, the algorithm are also suitable for higher dimensional topologies such as hypercubes.

PETSC2.0 is a software toolkit for portable, parallel (and serial) numerical solution of partial differential equations and minimization problems. It includes software for the solution of linear and nonlinear systems of equations. These codes are written in a data-structure-neutral manner to enable easy reuse and flexibility.

I. [6] The Work-Time (W-T) presentation of EREW sequence reduction (Algorithm 2 in PRAM handout) has work complexity WW(nn) = Ο(nn) and step complexity SS(nn) = Ο(lgnn). Following the strategy of Brent’s theorem, the translation of this algorithm will yield a pp processor EREW PRAM program with running time TTCC(nn,pp) = Ο(nn pp ⁄ + lgnn) (a) Construct an alternate sequence reduction algorithm directly for the bare bones EREW PRAM with running time TTCC(nn,pp) = Ο(nn pp ⁄ + lg pp). (b) Explain why your solution to (a) cannot be expressed in the W-T model.