Associative Graph Data Structures with an Efficient Access via AVB+trees

This paper introduces a new efficient associative graph data structure with efficient access to all stored data inspired by biological neural networks and associative brain-like approaches. It also introduces new self-balancing, self-organizing, and self-sorting AVB+trees which not only store data but it also allows for replacing many search operations with this structure. This structure aggregates representations of all duplicated of values and objects. It also allows for faster computation of many useful functions as medians, average, minima, maxima, neighbor values in the defined order etc. It always stores all data in order for all attributes simultaneously. Automatic aggregations of duplicates allow it for access to all stored data in less than logarithmic time. These associative structures can also be successfully used as a kind of artificial neural network for classification, clustering, various inferences, estimation of similarities, differences, or correlations of the stored objects.