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An efficient parallel construction of optimal independent spanning trees on hypercubes
Author(s)
Date Issued
December 1, 2012
Type
Article
Abstract
Reliable data broadcasting on parallel computers can be achieved by applying more than one independent spanning tree (IST). Using k-IST-based broadcasting from root r on an interconnection network (N=2 k) provides k-degree fault tolerance in broadcasting, while construction of optimal height k-ISTs needs more time than that of one IST. In the past, most research focused on constructing k ISTs on the hypercube Qk, an efficient communication network. One sequential approach utilized the recursive feature of Qk to construct k ISTs working on a specific root (r)=0 in O(kN) time. Another parallel approach was introduced for generating k ISTs with optimal height on Qk, based on HDLS (Hamming Distance Latin Square), single pointer jumping, which is applied for a source (r)=0 in O( k2) time for successful broadcasting in O(k). For broadcasting from r≠0, those existing approaches require a special routine to reassign new nodes' IDs for logical r=0. This paper proposes a flexible and efficient parallel construction of k ISTs with optimal height on Qk, a generalized approach, for an arbitrary root (r=0,1,2,..., or 2 k-1) in O(k) time. Our focus is to introduce the more efficient time (O(k)) of preprocessing, based on double pointer jumping over O( k2) of the HDLS approach. We also prove that our generalized parallel k-IST construction (arbitrary r) with optimal height on Qk is correctly set in efficient O(k) time. Finally, experiments were performed by simulation to investigate the fault-tolerance effect in reliable broadcasting. Experimental results showed that our efficient ISTs yielded 10%-20% fault tolerance for successful broadcasting (on N=16-1024 PEs). © 2012 Elsevier Inc. All rights reserved.
Citation
Journal of Parallel and Distributed Computing, 72(12), 1713-1724, 2012