NDLI: Three-Stage Generalized Connectors

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Three-Stage Generalized Connectors

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Karp, Richard M.
Copyright Year	1992
Abstract	An acyclic directed network with n sources and m sinks is called a generalized connector if, for any request pattern in which each sink asks to be connected to some source, the required configuration of noninterfering connecting paths can be set up. This paper presents new families of two- and three-stage connection networks and gives a method of establishing that particular networks in these families are generalized connectors. This method is based on the Erds probabilistic method and consists of two steps: 1. First it is proven that a given network is a generalized connector provided that certain events in a probability space $\Omega $ are of sufficiently low probability. 2. Then it is shown that the probabilities of these events are indeed sufficiently small.For the family of designs presented in Section 5, the second step is accomplished by explicitly calculating the probabilities of the events in question, using dynamic programming; these calculations provide rigorous proofs that the designs are correct. However, for the more economical designs of Section 6, the probabilities of the events in question are not calculated exactly, but instead are estimated by drawing pseudo-random samples from the probability space $\Omega $. Thus, we have only a statistical proof (albeit a very convincing one) of the correctness of these designs.For certain choices of n and m the most efficient three-stage generalized connectors currently known are obtained.
Starting Page	259
Ending Page	272
Page Count	14
File Format	PDF
ISSN	08954801
DOI	10.1137/0405020
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	5
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-08
Access Restriction	Subscribed
Subject Keyword	generalized connector connection network probabilistic method
Content Type	Text
Resource Type	Article
Subject	Mathematics

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