Optimal Tradeoffs Between Size and Slowdown for Universal Parallel Networks

Authors:
F. Meyer Auf Der Heide;M. Storch;R. Wanka
Affiliations:
Department of Mathematics and Computer Science and Heinz Nixdorf Institute, Paderborn University, D-33095 Paderborn, Germany fmadh@uni-paderborn.de, wanka@uni-paderborn.de, DE;Department of Mathematics and Computer Science and Heinz Nixdorf Institute, Paderborn University, D-33095 Paderborn, Germany fmadh@uni-paderborn.de, wanka@uni-paderborn.de, DE;Department of Mathematics and Computer Science and Heinz Nixdorf Institute, Paderborn University, D-33095 Paderborn, Germany fmadh@uni-paderborn.de, wanka@uni-paderborn.de, DE
Venue:
Theory of Computing Systems
Year:
1997

Citing 17
Cited 0

Efficient simulations among several models of parallel computers

SIAM Journal on Computing
Sorting in c log n parallel steps

Combinatorica
Tight bounds on the complexity of parallel sorting

IEEE Transactions on Computers
Optimal simulations by Butterfly Networks

STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Work-preserving emulations of fixed-connection networks

STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
On the computational equivalence of hypercube-derived networks

SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Introduction to parallel algorithms and architectures: array, trees, hypercubes

Introduction to parallel algorithms and architectures: array, trees, hypercubes
New graph decompositions and fast emulations in hypercubes and butterflies

SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Deterministic sorting in nearly logarithmic time on the hypercube and related computers

Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Bandwidth-based lower bounds on slowdown for efficient emulations of fixed-connection networks

SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Optimal emulations by butterfly-like networks

Journal of the ACM (JACM)
On the slowdown of efficient simulations of multibutterflies on butterflies and butterfly-derived networks

Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
A Permutation Network

Journal of the ACM (JACM)
An Efficient General-Purpose Parallel Computer

Journal of the ACM (JACM)
Time-Optimal Simulations of Networks by Universal Parallel Computers

STACS '89 Proceedings of the 6th Annual Symposium on Theoretical Aspects of Computer Science
Optimal Emulation of Meshes on Meshes of Trees

Euro-Par '95 Proceedings of the First International Euro-Par Conference on Parallel Processing
Universal emulations with sublogarithmic slowdown

SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

A parallel processor network is called n-universal with slowdown s if it can simulate each computation of each constant-degree processor network with n processors with slowdown s. We prove the following lower bound tradeoff: for each constant-degree n-universal network of size m with slowdown s, $m\cdot s=\Omega(n\log m)$ holds. Our tradeoff holds for a very general model of simulations. It covers all previously considered models and all known techniques for simulations among networks. For $m\ge n$ , this improves a previous lower bound by a factor of $\log\log n$ , proved for a weaker simulation model. For m , this is the first nontrivial lower bound for this problem. In this case this lower bound is asymptotically tight.