TY - JOUR

T1 - Impossibility results for weak threshold networks

AU - Busch, Costas

AU - Mavronicolas, Marios

N1 - Funding Information:
* Some of the results in this paper were announced in preliminary form in the conference version of [ 61. * Corresponding author. Partially supported by ESPRIT III Basic Research Project # 8 144 - LYDIA (“Load Balancing on High Performance Parallel and Distributed Systems”), and by funds for the promotion of research at University of Cyprus (research projects “Load Balancing Problems on Shared-Memory Multiprocessor Architectures” and “Distributed, Parallel, and Concurrent Computations”). Part of the work of this author was done while visiting Institute of Computer Science, Foundation for Research and Technology - Hellas. ’ Supported by NSF research grants DMS 95-05949 and CCR 96-13785. Part of the work of this author was done while at Department of Computer Science, University of Crete, and Institute of Computer Science, Foundation for Research and Technology - Hellas.

PY - 1997/7/28

Y1 - 1997/7/28

N2 - It is shown that a weak threshold network (in particular, threshold network) of width w and depth d cannot be constructed from balancers of width p0, p1, . . . , pm-1, if w does not divide Pd, where P is the least common multiple of p0, p1, . . . , pm-1. This holds regardless of the size of the network, as long as it is finite, and it implies a lower bound of logp w on its depth. More strongly, a lower bound of logpmax w is shown on the length of every path from an input wire to any output wire that exhibits the threshold property, where pmax is the maximum among p0, p1, . . . , Pm-1.

AB - It is shown that a weak threshold network (in particular, threshold network) of width w and depth d cannot be constructed from balancers of width p0, p1, . . . , pm-1, if w does not divide Pd, where P is the least common multiple of p0, p1, . . . , pm-1. This holds regardless of the size of the network, as long as it is finite, and it implies a lower bound of logp w on its depth. More strongly, a lower bound of logpmax w is shown on the length of every path from an input wire to any output wire that exhibits the threshold property, where pmax is the maximum among p0, p1, . . . , Pm-1.

KW - Distributed computing

KW - Impossibility results

KW - Parallel processing

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U2 - 10.1016/s0020-0190(97)00096-3

DO - 10.1016/s0020-0190(97)00096-3

M3 - Article

AN - SCOPUS:0006891830

VL - 63

SP - 85

EP - 90

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 2

ER -