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...
This paper discusses the relation among four problems: graph testing, DNA complex screening, superimposed codes and secure key distribution. We prove a surprising equivalence relat...
d Abstract) Noga Alon1, , Michael Capalbo2, , Yoshiharu Kohayakawa3, , Vojtˇech R¨odl4,† , Andrzej Ruci´nski5,‡ , and Endre Szemer´edi6,§ 1 Department of Mathematics, Raym...
Noga Alon, Michael R. Capalbo, Yoshiharu Kohayakaw...
The quantum query complexity of searching for local optima has been a subject of much interest in the recent literature. For the d-dimensional grid graphs, the complexity has been...
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...