Applications of Metric Spaces in Computational Complexity Theory

Abstract

Computational complexity theory heavily relies on b-dislocatedmetric spaces, quasi-metric spaces, and partialmetric spaces for structuring algorithms and evaluating their efficiency. These mathematical frameworks contribute to performance evaluation, ensuring effective problem classification and optimization techniques. This paper investigates how these metric spaces contribute to Computational complexity theoretical aspests such as algorithm efficiency,complexity analysis and other applications. For example, we show that the solution to the divide and conquer recurrence equation is unique regardless of the size of of a nutural number used to split the problem and the complexity distance function can be used to provide asymptotic upper bound of the divide and conquer recurrence. In addition,we use b-relaxed triangle inequality of b-dislocated metric to measure similarity between documents, videos and pictures.