Revision #1 Authors: Yosi Ben-Asher, Ilan Newman

Accepted on: 20th March 1997 00:00

Downloads: 2423

Keywords:

The architecture of 'mesh of buses'

is an important model in parallel computing.

Its main advantage is that the additional broadcast capability can be used

to overcome the main disadvantage of the mesh, namely

its relatively large diameter.

We show that the addition of buses indeed accelerates routing times.

Furthermore, unlike in the `store and

forward' model, the routing time becomes proportional to the network load,

resulting in decreasing in routing time for a smaller number of packets.

We consider 1-1 routing of $m$ packets in

a $d$-dimensional mesh with $n^d$ processors and $d\cdot n^{d-1}$

buses (one per row and column).

The two standard models of accessing the buses are considered and

compared: CREW, in which only one processor may transmit at any

given time on a given bus, and the CRCW

model in which several processors may attempt to transmit at the

same time (getting a noise signal as a result).

We design a routing algorithm that routes $m$ packets

in the CREW model in $O(m^{\frac 1 d} + n^{\frac 1 {d+1}})$

steps. This result holds for $m \leq n^{\frac{2d}{3}}$ for $d \geq 3$

and unconditionally for $d=2$.

A matching lower bound is also proved.

In the CRCW case we show an algorithm of $O(m^{\frac 1 d}

\log n)$ and a lower

bound of $\Omega(m^{\frac 1 d})$. It is shown that the difference between

the models is essentially due to the improved capability of estimating

threshold functions in the CRCW case.

TR96-053 Authors: Yosi Ben-Asher, Ilan Newman

Publication: 14th October 1996 12:17

Downloads: 2542

Keywords:

The architecture of 'mesh of buses' is an important model in parallel computing. Its main advantage is that the additional broadcast capability can be used to overcome the main disadvantage of the mesh, namely its relatively large diameter. We show that the addition of buses indeed accelerates routing times. Furthermore, unlike in the `store and forward' model, the routing time becomes proportional to the network load, result