Scheduled System Maintenance:
On Monday, April 27th, IEEE Xplore will undergo scheduled maintenance from 1:00 PM - 3:00 PM ET (17:00 - 19:00 UTC). No interruption in service is anticipated.
By Topic

On the validity of a reduction of reliable network design to a graph extremal problem

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

4 Author(s)

An undirected connected graph having failure probabilities associated with each edge is a classic model for network reliability studies. The network reliability is defined as the probability that the graph remains connected despite edge failures. It is known that the problem of calculating the network reliability is NP -hard, even when the edge failures are equal and independent. Herein, we consider synthesis problems for the equal edge failure rate case. Specifically, we treat the case where the number of points p , the number of edges q , and the edge failure rate \rho are given; the synthesis problem is to find a p -point, q -edge graph that maximizes the network reliability for the given \rho . A simple intuitive argument indicates that this synthesis problem can be reduced to a solvable graph extremal question when \rho is small. Here we formalize this observation by giving explicit formulas for a range (0 < \rho \leq \rho_0) of \rho values which allows the reliability synthesis problem to be reduced to this graph extremal question. We also discuss the possibility of extending this type of result to all possible \rho values (0 < \rho{\leq}1) thereby obtaining a uniformly optimum graph. The problem of ascertaining the existence of such graphs remains open; however, we suggest several possible approaches. We also relate some reliability questions to unsolved graph extremal problems involving the maximum and minimum number of spanning trees among all p -point, q -edge graphs. Several conjectures regarding these latter problems are presented.

Published in:

Circuits and Systems, IEEE Transactions on  (Volume:34 ,  Issue: 12 )