Combinatorial Optimization of CAD Systems

Abstract

Combinatorial optimization of CAD systems and their applications in information technologies regarded. Combinatorial cyclic sequences, namely the Ideal Ring Bundles (IRBs), are of very useful mathematical configurations for finding optimal solutions for wide classes of technological problems in CAD and information technologies. IRBs are cyclic sequences of numbers, which form perfect partitions of a finite spatial interval of sets, where sums of connected sub-sequences of an IRB enumerate the set of integers exactly r-times. Remarkable properties of one- and multidimensional IRBs allow configuring combinatorial graphs of optimal engineering devices or systems with non-uniform structure (e.g. rotational speed to code converters) with well positioning precision and resolving ability, using novel designs based on the combinatorial configurations. These design techniques make it possible to organize systems with optimal placement of structural elements in spatially or temporally distributed systems, including the appropriate algebraic constructions based on cyclic groups in extensions of Galois fields.