Journal of Interconnection Networks

We comment on the paper “Extremal Cayley digraphs of finite Abelian groups” [Intercon. Networks 12 (2011), no. 1-2, 125–135]. In particular, we give some counterexamples to the results presented there, and provide a correct result for degree two.

In this paper, we present a novel real-time analysis framework for AFDX (Avionics Full Duplex Switched Ethernet) networks. The framework, based on end-to-end response time analysis, calculates not only delay bounds, but also the maximum jitter for each VL (Virtual Link) at each hop, which is necessary according to the AFDX standard. Moreover, the framework supports multicasting, i.e., VLs with several paths, and VLs with arbitrary delay bounds, i.e., shorter, longer, or equal to their periods. An analysis method to calculate the worst-case buffer population is included in the framework, as it is important to guarantee that no buffer-overflow occurs. With a performance surpassing that of Network Calculus and comparable with Trajectory Approach, our framework presents a good choice due to its many features and its foundation in well-accepted analysis methods.

The hypercube is one of the most popular interconnection networks due to its structural regularity, potential for parallel computation of various algorithms, and the high degree of fault tolerance. In this paper, we introduce a tree called l-sibling trees and the main results obtained in this paper are: (1) For r ≥ 1, the minimum wirelength of embedding r-dimensional hypercube into r-dimensional l-sibling tree. (2) For r ≥ 1, embedding of r-dimensional extended l-sibling tree into caterpillar with minimum dilation. (3) Based on the proof of (1), we provide an O(r)-linear time algorithm to compute the minimum wirelength of embedding r-dimensional hypercube into r-dimensional l-sibling tree.

Determining the fractal dimension d_B of a complex network requires computing N(s), the minimal number of boxes of size s needed to cover the network. While effective approximation methods for this problem are known, the computation of a lower bound on N(s) has not been studied. We show that a lower bound can be obtained by formulating the covering problem as an uncapacitated facility location problem, and applying dual ascent to the dual of its linear programming relaxation. We illustrate the method on a small example, and provide numerical results on some larger problems. The upper and lower bounds on N(s) can be used to define a linear program which yields upper and lower bounds on d_B.

A Signed graph (or sigraph in short) is an ordered pair S = (G, σ), where G is a graph G = (V, E) and σ : E → {+, −} is a function from the edge set E of G into the set {+, −}. For a positive integer n > 1, the unitary Cayley graph X_n is the graph whose vertex set is Z_n, the integers modulo n and if U_n denotes set of all units of the ring Z_n, then two vertices a, b are adjacent if and only if a − b ∈ U_n. In this paper, we have obtained a characterization of balanced and clusterable unitary Cayley ring sigraph . Further, we have established a characterization of canonically consistent unitary Cayley ring sigraph , where n has at most two distinct odd primes factors. Also sign-compatibility has been worked out for the same.