Lower Bounds on the Loading of Multiple Bus Networks for Binary Tree Algorithms
IEEE Transactions on Computers
Routing Algorithms on the Bus-Based Hypercube Network
IEEE Transactions on Parallel and Distributed Systems
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A binary-tree algorithm, Bin(n), proceeds level-by-level from the leaves of a 2 n -leaf balanced binary tree to its root. This paper deals with running binary-tree algorithms on multiple bus networks (MBNs) in which processors communicate via buses. Every binary-tree "MBN" has a degree (maximum number of buses connected to a processor) of at least 2. There exists a degree-2 MBN [15] for Bin(n) that has a loading (maximum number of processors connected to a bus) of T(n). For any MBN that runs Bin(n) optimally, the loading was recently proved to be ?(n 1/2 ) [3]. In this paper, we narrow the gap between the results in [3, 15] by deriving a tighter lower bound of (n 2/3 ). We also establish a tradeoff between the speed and loading of degree-2 binary-tree MBNs.