Wireless network topologies change over time and maintaining routes requires
frequent updates. Updates are costly in terms of consuming throughput available
for data transmission, which is precious in wireless networks. In this paper,
we ask whether there exist low-overhead schemes that produce low-stretch
routes. This is studied by using the underlying geometric properties of the
connectivity graph in wireless networks.
This paper addresses the problem of finding the nearest neighbor (or one of
the R-nearest neighbors) of a query object q in a database of n objects. In
contrast with most existing approaches, we can only access the ``hidden'' space
in which the objects live through a similarity oracle. The oracle, given two
reference objects and a query object, returns the reference object closest to
the query object. The oracle attempts to model the behavior of human users,
capable of making statements about similarity, but not of assigning meaningful
numerical values to distances between objects.