scholarly journals Some new optimal and suboptimal infinite families of undirected double-loop networks

2006 ◽  
Vol Vol. 8 ◽  
Author(s):  
Bao-Xing Chen ◽  
Ji-Xiang Meng ◽  
Wen-Jun Xiao
Keyword(s):  
Necessary Conditions ◽  
Undirected Graph ◽  
Double Loop ◽  
Circulant Graph ◽  
Double Loop Network ◽  
International Audience ◽  
Sufficient And Necessary Conditions ◽  
Loop Network ◽  
Double Loop Networks ◽  
Positive Integers

International audience Let n, s be positive integers such that 2 ≤ s < n and s = n/2 . An undirected double-loop network G(n; 1, s) is an undirected graph (V,E), where V =Zn={0, 1, 2, . . . , n−1} and E={(i, i+1 (mod n)), (i, i+s (mod n)) | i ∈ Z}. It is a circulant graph with n nodes and degree 4. In this paper, the sufficient and necessary conditions for a class of undirected double-loop networks to be optimal are presented. By these conditions, 6 new optimal and 5 new suboptimal infinite families of undirected double-loop networks are given.

DIAMETER FORMULAS FOR A CLASS OF UNDIRECTED DOUBLE-LOOP NETWORKS

2005 ◽  
Vol 06 (01) ◽  
pp. 1-15 ◽  
Author(s):  
BAOXING CHEN ◽  
WENJUN XIAO ◽  
BEHROOZ PARHAMI
Keyword(s):  
Closed Form ◽  
Open Problem ◽  
Time Algorithm ◽  
Double Loop ◽  
Network Diameter ◽  
Double Loop Network ◽  
Node Network ◽  
Loop Network ◽  
Double Loop Networks ◽  
Closed Form Formula

An n-node network, with nodes numbered 0 to n-1, is an undirected double-loop network with chord lengths 1 and s(2≤s<n/2) when each node i(0≤i<n) is connected to each of the four nodes i±1 and i±s via an undirected link; all node-index expressions are evaluated modulo n. Let n=qs+r, where r(0≤r<s) is the remainder of dividing n by s. Furthermore, let s=ar+b, where b(0≤b<r) is the remainder of dividing s by r. In this paper, we provide closed-form formulas for the diameter of a double-loop network for the case q>r and for a subcase of the case q≤r when b≤aq+1. In the complementary subcase of q≤r, when b>aq+1, network diameter can be derived by applying the O(log n)-time algorithm of Zerovnik and Pisanski (J. Algorithms, Vol. 14, pp. 226-243, 1993). Obtaining a closed-form formula for diameter of the double-loop network in the latter subcase remains an open problem.

Reliabilities of Double-Loop Networks

1991 ◽  
Vol 5 (3) ◽  
pp. 255-272 ◽  
Author(s):  
F.K. Hwang ◽  
Wen-Ching Winnie Li
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Double Loop ◽  
Reliability Model ◽  
Double Loop Network ◽  
Strongly Connected ◽  
Loop Network ◽  
Double Loop Networks ◽  
Link Connectivity

A double-loop network G(h1, h2) has n nodes represented by the n residues modulo n and 2n links given by i ↦i + h1, i ↦ i + h2, i = 0,1,…,n – 1.We consider the reliability model where each link fails independently with probability p, the nodes always work, and the network fails if it is not strongly connected. There exists no known polynomial time algorithm to compute the reliabilities of general double-loop networks. When p is small, the reliability is dominated by the link connectivity. As all strongly connected double.loop networks have link connectivity exactly 2, a finer measure of reliability is needed. In this paper we give such a measure and show how to use it to obtain the most reliable double-loop networks.

scholarly journals An efficient algorithm to find a double-loop network that realizes a given L-shape

2006 ◽  
Vol 359 (1-3) ◽  
pp. 69-76 ◽  
Author(s):  
Chiuyuan Chen ◽  
James K. Lan ◽  
Wen-Shiang Tang
Keyword(s):  
Efficient Algorithm ◽  
Double Loop ◽  
Double Loop Network ◽  
Loop Network

SOME COMBINATORIAL PROPERTIES OF MIXED CHORDAL RINGS

2003 ◽  
Vol 04 (01) ◽  
pp. 3-16 ◽  
Author(s):  
S. K. CHEN ◽  
F. K. HWANG ◽  
Y. C. LIU
Keyword(s):  
Double Loop ◽  
Combinatorial Properties ◽  
Double Loop Network ◽  
Hamiltonian Circuits ◽  
Loop Network ◽  
Chordal Ring

We propose a new network called the mixed chordal ring where the amount of hardware and its structure are very comparable to the (directed) double-loop network, and yet can achieve a better diameter. We also investigated other combinatorial properties such as connectivity and hamiltonian circuits in the mixed chordal ring.

[+h]-Link Prior Routing Strategy for Double-Loop Network

2009 ◽  
Vol 31 (3) ◽  
pp. 536-542
Author(s):  
Mu-Yun FANG ◽  
Yu-Gui QU ◽  
Bao-Hua ZHAO
Keyword(s):  
Double Loop ◽  
Routing Strategy ◽  
Double Loop Network ◽  
Loop Network

scholarly journals Necessary and sufficient conditions for oscillations of linear delay partial difference equations

1998 ◽  
Vol 1 (4) ◽  
pp. 265-268 ◽  
Author(s):  
B. G. Zhang ◽  
S. T. Liu
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Partial Difference Equation ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
All Solutions ◽  
Linear Delay ◽  
Sufficient And Necessary Conditions ◽  
Necessary And Sufficient ◽  
Positive Integers

This paper is concerned with the linear delay partial difference equationAm,n=∑i=1upiAm−ki,n−li+∑j=1vqjAm+τj,n+σj, wherepiandqjarer×rmatrices,Am,n=(am,n1,am,n2, …,am,nr)T, ki, li , τjandσjare nonnegative integers,uandvare positive integers. Sufficient and necessary conditions for all solutions of this equation to be oscillatory componentwise are obtained.

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