Towards Distance Ordering in Large Robot and Sensor Networks

Localization in robot networks has been extensively studied and in the absence of sophisticated sensors and high connectivity, it remains a challenging problem. We study the problem of distance ordering i.e. comparing any two distances in a large robot network and deciding which one is larger. Given a localized graph, distance ordering is trivial but the question we attempt to answer is whether it can be done without localization. We first present a survey of results on the localizability of a network given a variety of inputs and infer that it is an NP-hard problem except in certain special scenarios. We then present some preliminary results on tackling distance ordering without localization.