Abstract: A method and apparatus for generating, manipulating, and displaying a universal set of data structures is disclosed. A Table Facility generates and stores tokens and a Logic Processor communicates with external host programs and performs arithmetic and logical manipulations of the tokens in response to requests from the host program. The tokens can be tested and used as any currently known data structure, including but not limited to binary trees and linked lists, as well as being versatile enough to emulate new data structures. The method used to create the data structures is such that many database operations, such as comparison of files and data or their merging, proceed much faster on the present invention than known in the art.

Abstract: The invention relates to method and apparatus for computing transitive closure and reachability in directed graphs. These are fundamental graph problems with many applications such as database query optimization. A random rank is applied to each node (or record or element, as the case may be) and the least rank reachable from each such node is determined. This least rank value reachable from a node is highly correlatable to the size of the reachable set. An estimator can therefore be applied to convert the least reachable rank value to an estimate of the size of the reachable set. The accuracy of the estimate can be increased by repeating the random rank assignments together with the least reachable rank determinations and averaging the results.