Cart (Loading....) | Create Account
Close category search window
 

d-separated paths in hypercubes and star graphs

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)
Qian-Ping Gu ; Dept. of Comput. Software, Univ. of Aizu, Fukushima, Japan ; Peng, S.

In this paper, we consider a generalized node disjoint paths problem: d-separated paths problem. In a graph G, given two distinct nodes s and t, two paths P and Q, connecting s and t, are d-separated if dG-{s,t}⩾d for any u∈P-{s,t} and v∈Q-{s,t}, where dG-{s,t}(u,v) is the distance between u and v in the reduced graph G-{s,t}. d-separated paths problem is to find as many d-separated paths between s and t as possible. In this paper, we give the following results on d-separated paths problems on n-dimensional hypercubes Hn and star graphs Gn. Given s and t in Hn, there are at least (n-2) 2-separated paths between s and t. (n-2) is the maximum number of 2-separated paths between s and t for d(s,t)⩾4. Moreover, (n-2) and separated paths of length at most d(s,t)+2 for d(s,t)<n and of length n for d(s,t)=n between s and t can be constructed in O(n2) optimal line. For d⩾3, d-separated paths in Hn do not exist. Given s and t in Gn, there are exactly (n-1) d-separated paths between s and t for 1⩽d⩽3 (n-1) 3-separated paths of length at most min{d(s,t)+4, d(Gn)+2} between s and t can be constructed in O(n2) optimal time, where d(Gn)=[3(n-1)/2]. For d⩾5 d-separated paths in Gn do not exist

Published in:

Algorithms &amp; Architectures for Parallel Processing, 1996. ICAPP 96. 1996 IEEE Second International Conference on

Date of Conference:

11-13 Jun 1996

Need Help?


IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.