Sorting in c log n parallel steps
Combinatorica
Tight bounds on the complexity of parallel sorting
IEEE Transactions on Computers
A bridging model for parallel computation
Communications of the ACM
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
An O(log N) deterministic packet-routing scheme
Journal of the ACM (JACM)
On-line Algorithms for Path Selectionin a Nonblocking Network
SIAM Journal on Computing
Improved routing and sorting on multibutterflies
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Scheduling Parallel Communication: The h-relation Problem
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
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In this paper we devise an optimal deterministic algorithm for routing h-relations on-line on an N-input/output multibutterfly. The algorithm, which is obtained by generalizing the circuit-switching techniques of [3], routes any h-relation with messages of X bits in O (h(X + log N)) steps in the bit model, and in O (h驴X/ log N驴 + log N) communication steps in the word model. Unlike other recently developed algorithms, our algorithm does not need extra levels of expanders, hence minimizes the layout area. Moreover the network topology does not depend on h.