Mossel and Ross raised the question of when a random coloring graph can be reconstructed from local information, namely, colorings (with multiplicity) balls given radius. In this article, we are concerned with 2-colorings vertices -dimensional hypercube, or equivalently Boolean functions. worst case, diameter required to reconstruct. However, situation for is dramatically different: show that a...

In this paper we consider the three-dimensional layout of hypercube networks. Namely, we study the problem of laying hypercube networks out on the three-dimensional grid with the properties that all nodes are represented as rectangular slices and lie on two opposite sides of the bounding box of the layout volume. We present both a lower bound and a layout method providing an upper bound on the ...

The Hales numbered n-dimensional hypercube and the corresponding adjacency matrix exhibit interesting recursive structures in n. These structures lead to a very simple proof of the well-known bandwidth formula for hypercube, whose proof was thought to be surprisingly difficult. A related problem called hypercube antibandwidth, for which Harper proposed an algorithm, is also reexamined in the li...

This paper describes a fault-tolerant routing mechanism to facilitate data routing in Torus embedded hypercube interconnection network subject to node failures in parallel computing. It is shown that by only using feasible paths routing can be substantially simplified. Though there are algorithms for fault tolerant communication in torus and hypercube networks, there exits no efficient algorith...

A new, fault-tolerant, scalable, and, modular virtual topology for lightwave networks employing wavelength division multiplexing is proposed. The proposed architecture is based on hypercube connected ring structure that enjoys the rich topological properties of hypercube, but it also overcomes one of its drawback. In a hypercube, the nodal degree increases with the number of nodes. Hence, the p...

-When designing wireless sensor networks, the process of establishing and distributing the secret keys securely and efficiently is very challenging due to the unpredictable network topology. Recently, hypercube virtual backbone approach has been used to provide efficient data gathering schemes for the wireless sensor networks. The hypercube attractive structure and topological properties provid...