By Topic

Cut-Set Intersections and Node Partitions

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

2 Author(s)
Buzacott, J.A. ; Department of Management Sciences; University of Waterloo; Waterloo, Ontario, N2L 3G1 CANADA. ; Chang, Jack S.K.

With any cut set of a graph can be associated a partition of the nodes into two cells. We show that each cut-set intersection term in the cut-set inclusion and exclusion formula can be associated with a k-cell partition of the nodes. Thus, the number of distinct terms in the cut-set inclusion and exclusion formula cannot exceed the number of partitions of the set of nodes. This leads to a simplified formula for graph reliability: the node partition formula, When finding the overall reliability in complete graphs no terms cancel, thus the number of terms is equal to the number of partitions. In other graphs we show that the number of non-cancelling terms in the cut-set inclusion and exclusion formula is equal to the number of minimal partition sets of the graph. It follows that cut-set inclusion and exclusion is inherently an inefficient method for the exact calculation of network reliability measures.

Published in:

Reliability, IEEE Transactions on  (Volume:R-33 ,  Issue: 5 )