APL2: at a glance
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
OLAP solutions: building multidimensional information systems
OLAP solutions: building multidimensional information systems
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A Fast Algorithm for Complete Subcube Recognition
ISPAN '97 Proceedings of the 1997 International Symposium on Parallel Architectures, Algorithms and Networks
An algorithm to compute all full-span sub arrays of a regular array
Proceedings of the 2003 conference on APL: stretching the mind
Generalized Hypercube and Hyperbus Structures for a Computer Network
IEEE Transactions on Computers
An algorithm to compute all full-span sub arrays of a regular array
Proceedings of the 2003 conference on APL: stretching the mind
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Using a radically new way of representing arrays, we present a formalism that expands (or decomposes) a regular array into a weighted sum of null arrays. We show that this "polynomial" expansion (1.16) exhaustively represents the regular full-span array sub structure of the original array. Full-span means full length in the dimensions used. The polynomial is a generating function whose coefficients of which count and indicate the shape of the regular full-span sub arrays of the given regular array. These results are all structural. They do not use knowledge of the particular data contents of the arrays. We apply this new decomposition to catenation and lamination and uncover some new insights into array structure.The decomposition and the algebraic results provide a unifying view and new formalism for regular multi-dimensional arrays. It has application wherever multi-dimensional arrays are used, particularly to generalized hyper cube architectures, OLAP hierarchical data structures, and array oriented languages. It subsumes some previous results. Some of these applications are indicated with their bibliography.There is a combinatorial argument on the shape vector that could generate the coefficients, but it does not give the structural insight of this approach.