We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geo...
In this paper we introduce a general strategy for approximating the solution to minimisation problems in random regular graphs. We describe how the approach can be applied to the m...
A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r-regular uniquely hamiltonian graphs when r > 22. This im...
Penny E. Haxell, Ben Seamone, Jacques Verstraë...
We consider the problem of finding a maximum independent set in a random graph. The random graph G, which contains n vertices, is modelled as follows. Every edge is included inde...
This paper presents improved approximation algorithms for the problem of multiprocessor scheduling under uncertainty (SUU), in which the execution of each job may fail probabilist...
Christopher Y. Crutchfield, Zoran Dzunic, Jeremy T...