Abstract

We develop alternative data structures for the representation of network optimization problems on massively parallel SIMD (i.e. Single Instruction Multiple Data) architectures. These data structures are used to implement a primal-dual algorithm for the optimization of a quadratic function subject to network constraints on the Connection Machine CM-2. In particular, two representations of arbitrary, sparse network topologies - a node-wise and an arc-wise representation - are compared with each other in terms of the efficiency with which certain primal-dual algorithms can be executed. Both implementations are also compared with the performance of the same algorithms when applied to dense, bipartite transportation problems. Particular attention is paid to communication efficiency. To this end, the problem of mapping the problem data to the Connection Machine hypercube network is investigated and a pre-computed, optimized, communication scheme is used. The results, collectively, show that very efficient implementations of network algorithms are possible on massively parallel architectures. This statement is true not only in solving dense, bipartite problems, but, even more importantly, in solving problems with arbitrary, sparse network topologies.

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