kevin@sun.uucp (Kevin Sheehan) (04/24/85)
<just a thought> There has been a recent discussion regarding various orders of "hypercube" topolgies in parallel computing. One of the topics of conversation was the influence of structure on communications (path lengths, node delay, etc.) One of the things that struck me was the analysis of path in a "square" structure. I have seen a discussion of cube and various N-dimensional equivalents, and the properties they posess. My fuel to the fire would be the addition of the property of simplest N-gon in the space as a model. As example, consider this contrast between the construction of "square" objects in a given space, and the simplest. dimension 0 1 point /1 point (obvious, but let's start simple) dimension 1 2 points = line /2 points = line dimension 2 4 points, 4 lines = square /3 points, three lines = triangle dimension 3 8 pts, 6 faces,12 lines = cube /4 pts, 4 triangles, 6 lines = tetrahedron dimension 4 16 pts, ... 8 cubes hypercube tesseract /5 pts ... 5 tetra's = polytetrahedron the mind boggles after that. Anyway, the simpler system seems to have the propery of being completely connected. ie, in a cube to get from one corner to the opposite, you have either 2 (same plane) or three (other corner) paths to cross. In a tetrahedron, all vertices (nodes) are directly connected. Now the match - what impact would this have on current topolgies suggested for the "hypercube" computers, and what impact on other things based on pure right angle reasoning? l & h, kev PS or the Zen alternative, am I full of *? - if replies are anatomical in nature, please be specific :-)