Algorithms to Realize an Arbitrary BPC Permutation in Chordal Ring Networks With Failures

Abstract

A family of regular graphs of degree 3, called chordal rings is presented as a possible candidate for the implementation of a distributed system and for fault-tolerant architectures. The symmetry of graphs makes it possible to determine message routing by using a simple distributed algorithm. Arbitrary data permutations are generally accomplished by sorting. For certain classes of permutations, however, there exist algorithms that are more efficient than the best sorting algorithm. One such class is the Bit Permute Complement (BPC) class of permutations. In this paper, we first develop algorithms requiring two token storage registers in each node to realize an arbitrary BPC permutation. We next evaluate its ability to realize BPC permutations in networks of arbitrary size by estimating the number of required routing steps when a single fault is present and when not.

Optimal processor mapping for linear-complement communication on hypercubes

“…Many studies have been based on store-and-forward routing, where the message latency is proportional to the product of the message length and the number of routing steps. Hence, most of them have concentrated on minimizing the number of routing steps in moving messages among processors [4], [16], [17], [18], [20], [21]. On the other hand, wormhole routing has been widely adopted recently due to its effectiveness in interprocessor communication [1], [2], [22].…”

“…Most of them focused on subsets of LCC, such as linear-complement permutation (LCP) and bit-permute-complement permutation (BPC). For example, Boppana and Raghavendra [4] considered LCPs on hypercubes, Nassimi and Sahni [20], [21] dealt with BPCs on meshes and hypercubes, and Masuyama [17], [18] dealt with BPCs on chordal rings and hypercubes. However, none of these methods can be applied to linear-complement scatter (LCS) or linear-complement gather (LCG).…”