Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the re...
A new random geometric graph model, the so-called secrecy graph, is introduced and studied. The graph represents a wireless network and includes only edges over which secure commun...
We study the expected topological properties of ˇCech and Vietoris-Rips complexes built on random points in Rd . We find higher dimensional analogues of known results for connect...
We maintain the maximum spanning tree of a planar point set, as points are inserted or deleted, in O(log3 n) time per update in Mulmuley's expected-case model of dynamic geom...