Connecting identifying codes and fundamental bounds

Abstract

Abstract-We consider the problem of generating a connected robust identifying code of a graph, by which we mean a subgraph with two properties: (i) it is connected, (ii) it is robust identifying, in the sense that the (subgraph-) induced neighborhoods of any two vertices differ by at least 2r + 1 vertices, where r is the robustness parameter. This particular formulation builds upon a rich literature on the identifying code problem but adds a property that is important for some practical networking applications. We concretely show that this modified problem is NP-complete and provide an otherwise efficient algorithm for computing it for an arbitrary graph. We demonstrate a connection between the the sizes of certain connected identifying codes and errorcorrecting code of a given distance. One consequence of this is that robustness leads to connectivity of identifying codes.

Locating-Domination and Identification

“…It is also possible to generalize these concepts to hypergraphs, and of course, some of these definitions can be combined, e.g., connected vertex-robust identifying codes [78].…”