A new "dual-view" diagram of array structure

ABSTRACT

First we present a new structural decomposition of regular arrays that is derived elsewhere [4]. Second, we list a few special cases of the decomposition. Finally we give 11 examples of arrays, their decomposition, their egg crate view, and their dual view (which better represents their true structure).We present this graphical presentation form (a diagrammatic notation) for a regular array. The notation is a "dual" of the usual "egg crate" view. This view makes clear and intuitive the otherwise unintuitive results derived from the newly found array expansion in [4]. The array expansion results are all structural therefore so are these pictorial results. They do not use knowledge of the particular data contents of the arrays.

REFERENCES

• 1: Bhuyan, L.N. and Agrawal, D.P. Generalized Hypercube and Hyperbus Structures for a Computer Network. IEEE transactions on computers, C-33 (4). 323--333 {April 1984}.
• 2: Hal Burch , Fikret Ercal, A Fast Algorithm for Complete Subcube Recognition, Proceedings of the 1997 International Symposium on Parallel Architectures, Algorithms and Networks (ISPAN '97), p.85, December 18-20, 1997
• 3: Fan, C.K. Re: Hypercubes and POW Solution, September 18--22. American Mathematical Monthly, 44. 18--22.
• 4: Ronald I. Frank , Fred Grossman, Regular array expansions in null arrays, with applications: zero is not nothing, 2002
• 5: F. Thomson Leighton, Introduction to parallel algorithms and architectures: array, trees, hypercubes, Morgan Kaufmann Publishers Inc., San Francisco, CA, 1991

INDEX TERMS

Primary Classification:
  E. Data
  E.1 DATA STRUCTURES

General Terms:
Documentation

Keywords:
array structure, connectivity, diagramming, null-array expansion, visualization