Efficient tilings of de Bruijn and Kautz graphs

Kautz and de Bruijn graphs have a high degree of connectivity which makes them ideal candidates for massively parallel computer network topologies. In order to realize a practical computer architecture based on these graphs, it is useful to have a means of constructing a large-scale system from smaller, simpler modules. In this paper we consider the mathematical problem of uniformly tiling a de Bruijn or Kautz graph. This can be viewed as a generalization of the graph bisection problem. We focus on the problem of graph tilings by a set of identical subgraphs. Tiles should contain a maximal number of internal edges so as to minimize the number of edges connecting distinct tiles. We find necessary and sufficient conditions for the construction of tilings. We derive a simple lower bound on the number of edges which must leave each tile, and construct a class of tilings whose number of edges leaving each tile agrees asymptotically in form with the lower bound to within a constant factor. These tilings make possible the construction of large-scale computing systems based on de Bruijn and Kautz graph topologies.Comment: 29 pages, 11 figure

Links between topography, wind, deflation, lakes and dust: The case of the Bodélé Depression, Chad

The Bodélé Depression, Chad is the planet's largest single source of dust. Deflation from the Bodélé could be seen as a simple coincidence of two key prerequisites: strong surface winds and a large source of suitable sediment. But here we hypothesise that long term links between topography, winds, deflation and dust ensure the maintenance of the dust source such that these two apparently coincidental key ingredients are connected by land-atmosphere processes with topography acting as the overall controlling agent. We use a variety of observational and numerical techniques, including a regional climate model, to show that: 1) contemporary deflation from the Bodélé is delineated by topography and a surface wind stress maximum; 2) the Tibesti and Ennedi mountains play a key role in the generation of the erosive winds in the form of the Bodélé Low Level Jet (LLJ); 3) enhanced deflation from a stronger Bodélé LLJ during drier phases, for example, the Last Glacial Maximum, was probably sufficient to create the shallow lake in which diatoms lived during wetter phases, such as the Holocene pluvial. Winds may therefore have helped to create the depression in which erodible diatom material accumulated. Instead of a simple coincidence of nature, dust from the world's largest source may result from the operation of long term processes on paleo timescales which have led to ideal conditions for dust generation in the world's largest dust source. Similar processes plausibly operate in other dust hotspots in topographic depressions

The Impact Of Writing Assignments In Business Education: Toward A Competitive Advantage In The Workplace

Twenty-first century organizations are increasingly becoming global information networks where the emphasis on written communication is growing exponentially. Effective writing skills are becoming more essential to workplace success and thus a central focus in business programs across the country. This article addresses writing issues in business education and how they relate to effective workplace writing. The article focuses on three essential factors - teaching writing to international students, faculty attitudes, and workplace writing and how each of these aid in producing students with the effective writing skills that add value to their potential employers