A weakness of next-hop routing is that following a link or router failure there may be no routes between some source-destination pairs, or packets may get stuck in a routing loop as the protocol operates to establish new routes. In this article, we address these weaknesses by describing mechanisms to...
We give a randomized O(n polylog n)-time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed ε > 0 and given n terminals in the plane with connection requests between some pairs of terminals, our scheme finds a (1 + ε) approximation to the minimum-length...
For an undirected n-vertex planar graph G with non-negative edge-weights, we consider the following type of query: given two vertices s and t in G, what is the weight of a min st-cut in G? We show how to answer such queries in constant time with O(n log⁴ n) preprocessing...
A recent result of Chepoi, Estellon and Vaxes [Disc. Comp. Geom. '07] states that any planar graph
of diameter at most 2R can be covered by a constant number of balls of size R; put another way, there
are a constant-sized subset of vertices within which every other vertex is...
We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The schemes run in O(n log n) time for graphs embedded on both orientable and nonorientable surfaces. This work generalizes the PTAS frameworks...