Abstract
Connectivity (of node-to-node) is used to examine the robustness of graphs. In some telecommunication networks, some switches are integrated into a logical switching area. In this case, we should examine node-to-area connectivity rather than node-to-node connectivity.
A new idea, NA (node-to-area)-connectivity, is proposed, and this paper shows that the problem of making a minimum NA-connected spanning subgraph of a given graph belongs to the class NP-hard. It also shows, however, that a near-optimum solution to this problem can be given by a linear-time algorithm. The concept of k-NA-connectivity is also introduced, and this paper shows that any k-NA-connected graph G=(V, E) has a sparse k-NA-connected spanning subgraph G'=(V, E') with |E|=O(k|V|). This is shown by presenting an O(|E|)-time algorithm to find one such subgraph. Although the problem of making a minimum k-NA-connected spanning subgraph of a given graph, of course, belongs to the class NP-hard, this problem can be given an approximate solution by the algorithm.
