An optimally data efficient isomorphism inference algorithm

Abstract

The time, space, and data complexity of an optimally data efficient isomorphism identification algorithm are presented. The data complexity, the amount of data required for an inference algorithm to terminate, is analyzed and shown to be the minimum possible for all possible isomorphism inference algorithms. The minimum data requirement is shown to be ⌈log₂ (n)⌉, and a method for constructing this minimal sequence of data is presented. The average data requirement is shown to be approximately 2 log₂(n). The time complexity is O(n²log₂(n)) and the space requirement is O(n²)