Construction of vertex-disjoint paths in alternating group networks

Abstract

The existence of parallel node-disjoint paths between any pair of nodes is a desirable property of interconnection networks, because such paths allow tolerance to node and/or link failures along some of the paths, without causing disconnection. Additionally, node-disjoint paths support high-throughput communication via the concurrent transmission of parts of a message. We characterize maximum-sized families of parallel paths between any two nodes of alternating group networks. More specifically, we establish that in a given alternating group network AN n , there exist n − 1 parallel paths (the maximum possible, given the node degree of n − 1) between any pair of nodes. Furthermore, we demonstrate that these parallel paths are optimal or near-optimal, in the sense of their lengths exceeding the internode distance by no more than four. We also show that the wide diameter of AN n is at most one unit greater than the known lower bound D + 1, where D is the network diameter.

Conditional diagnosability of alternating group networks

“…Chen et al [24] presented an optimal routing algorithm for this class of networks. Zhou, Xiao and Parhami [25] further expanded these results on AN n by constructing containers of the maximum width, deriving the best containers, and then computed the wide diameter and fault diameter for AN n . Each alternating group network The comparison diagnosis strategy can be modelled as…”

Equal relation between the extra connectivity and pessimistic diagnosability for some regular graphs

“…For each i ∈ [n], AN i n is isomorphic to AN n−1 . By Theorem 1 in [44], AN n is (n − 1)-regular and (n − 1)-connected. (1) Each vertex in AN n has exactly one extra neighbor.…”

The 4-component connectivity of alternating group networks

“…In what follow, we shall present some properties of AN n , which will be used later. For more properties on alternating group networks, we refer to [6,13,19,30,31]. [13,30,31]) For AN n with n 4 and i, j ∈ Z n with i = j, the following holds:…”