We consider one-to-one embeddings of the n-dimensional hypercube into grids with 2n vertices and present lower and upper bounds and asymptotic estimates for minimal dilation, edge-congestion, and their mean values. We also introduce and study two new cost-measures for such embeddings, namely the sum over i = 1, ..., n of dilations and the sum of edge congestions caused by the hypercube edges of...

This paper presents a technique for approximating, up to any precision, the set of subgame-perfect equilibria (SPE) in repeated games with discounting. The process starts with a single hypercube approximation of the set of SPE payoff profiles. Then the initial hypercube is gradually partitioned on to a set of smaller adjacent hypercubes, while those hypercubes that cannot contain any SPE point ...

A well-known framework by Fagin, Halpern, Moses and Vardi models knowledge-based agents as \Inter-preted Systems". In this paper we analyse a particular class of interpreted systems, which we call hypercube systems, that share information among themselves. Hypercube systems arise by taking the full Cartesian product of the state space of interpreted systems. We analyse hypercube systems by taki...

The hypercube parallel architecture is one of the most popular interconnection networks due to many of its attractive properties and its suitability for general purpose parallel processing. An attractive version of the hypercube is the crossed cube. It preserves the important properties of the hypercube and most importantly reduces the diameter by a factor of two. In this paper, we show the abi...

We inductively describe an embedding of a complete ternary tree Th of height h into a hypercube Q of dimension at most d(1.6)he + 1 with load 1, dilation 2, node congestion 2 and edge congestion 2. This is an improvement over the known embedding of Th into Q. And it is very close to a conjectured embedding of Havel [3] which states that there exists an embedding of Th into its optimal hypercube...

This is a survey on hypercube embeddable semimetrics and the link with designs. We investigate, in particular, the variety of hypercube embeddings of the equidistant metric. For some parameters, it is linked with the question of existence of projective planes or Hadamard matrices. The problem of testing whether a semimetric is hyper-cube embeddable is NP-hard in general. Several classes of semi...

We consider two shellings of the boundary of the hypercube equivalent if one can be transformed into the other by an isometry of the cube. We observe that a class of indecomposable permutations, bijectively equivalent to standard double occurrence words, may be used to encode one representative from each equivalence class of the shellings of the boundary of the hypercube. These permutations thu...