Balanced Cut Approximation in Random Geometric Graphs [chapter]

Josep Diaz, Fabrizio Grandoni, Alberto Marchetti Spaccamela
2006 Lecture Notes in Computer Science  
A random geometric graph G(n, r) is obtained by spreading n points uniformly at random in a unit square, and by associating a vertex to each point and an edge to each pair of points at Euclidian distance at most r. Such graphs are extensively used to model wireless ad-hoc networks, and in particular sensor networks. It is well known that, over a critical value of r, the graph is connected with high probability. In this paper we study the robustness of the connectivity of random geometric graphs
more » ... in the supercritical phase, under deletion of edges. In particular, we show that, for a sufficiently large r, any cut which separates two components of Θ(n) vertices each contains Ω(n 2 r 3 ) edges with high probability. We also present a simple algorithm that, again with high probability, computes one such cut of size O(n 2 r 3 ). From these two results we derive a constant expected approximation algorithm for the β-balanced cut problem on random geometric graphs: find an edge cut of minimum size whose two sides contain at least β n vertices each.
doi:10.1007/11940128_53 fatcat:oyo3shbv7fgyzixngxsdydc554