Work-Efficient Routing Algorithms for Rearrangeable Symmetrical Networks

• Authors: Hasan Çam;José A. B. Fortes
• Venue: IEEE Transactions on Parallel and Distributed Systems
• Year: 1999

The work performed by a parallel algorithm is the product of its running time and the number of processors it requires. This paper presents work-efficient (or cost-optimal) routing algorithms to determine the switch settings for realizing permutations on rearrangeable symmetrical networks such as Benes and the reduced $\Omega_N \Omega_N^{-1}$. These networks have $2n-1$ stages with $N= 2^n$ inputs/outputs, each stage consisting of $N/2$ crossbar switches of size ($2 \times 2 $). Previously known parallel routing algorithms for a rearrangeable network with $N$ inputs determine the states of all switches recursively in $O(n)$ iterations using $N$ processors. Each iteration determines the switch settings of at most two stages of the network and requires at least $O(n)$ time on a computer of $N$ processors, regardless of the type of its interconnection network. Hence, the work of any previously known parallel routing algorithm equals at least $O( N n^2 )$ for setting up all the switches of a rearrangeable network. The new routing algorithms run on a computer of $p$ processors, $1 \leq p \leq N/n$, and perform work $O(Nn)$. Moreover, because the range of $p$ is large, the new routing algorithms do not have to be changed in case some processors become faulty.