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Faulttolerant routing for pyramid networks using the least layer minimal routing method
 Computer Systems: Science & Engineering
, 2003
"... Pyramid networks have long been proposed for parallel processing. However, when the network contains multiple pairs of source and destination nodes, it is often difficult to use the pyramid efficiently since most of the algorithms try to simultaneously use the apex for each pair of nodes. Therefore, ..."
Abstract

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Pyramid networks have long been proposed for parallel processing. However, when the network contains multiple pairs of source and destination nodes, it is often difficult to use the pyramid efficiently since most of the algorithms try to simultaneously use the apex for each pair of nodes. Therefore, there may exist a severe bottleneck in such circumstances. We propose a Least Level Minimal Routing (LLMR) scheme for releasing the bottleneck in pyramid networks. At each vertex, the algorithm using LLMR needs only O(n) time to determine the shortest path from the source to the destination, where n denotes the number of levels in the nonfaulty pyramid network. Besides, LLMR releases the apex from almost all transmission load for any pair of nodes. Furthermore, it reduces enormously the traffic in higher levels of the pyramid. We also provide pointtopoint node disjoint parallel routing algorithm in pyramid networks, where the lengths of the paths are at most 4n2 steps. Keywords pyramid networks, fault tolerant, minimal routing, load balancing. 1
Rainbow connection number in triangular pyramids
"... Rainbow connection number of a connected graph G is the minimum number of colours needed to colour the edges of G, so that every pair of nodes is connected by at least one path whose edges have distinct colours. In this paper, we find the rainbow connection number for a triangular pyramid. ..."
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Rainbow connection number of a connected graph G is the minimum number of colours needed to colour the edges of G, so that every pair of nodes is connected by at least one path whose edges have distinct colours. In this paper, we find the rainbow connection number for a triangular pyramid.