Clustering, Encoding and Diameter Computation Algorithms for Multidimensional Data

TL;DR

This paper introduces new algorithms for multidimensional data clustering, diameter computation, and string processing, with thorough theoretical analysis and some experimental evaluation, advancing methods for complex data analysis tasks.

Contribution

It presents novel algorithms for multidimensional clustering, diameter calculation with a new distance function, and string encoding and substring counting, with both theoretical and experimental insights.

Findings

Algorithms are theoretically analyzed for correctness and efficiency.

Some algorithms are validated through experimental evaluation.

The methods improve existing approaches for multidimensional and string data processing.

Abstract

In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We also consider two string (1D data) processing problems, regarding an optimal encoding method and the computation of the number of occurrences of a substring within a string generated by a grammar. The algorithms have been thoroughly analyzed from a theoretical point of view and some of them have also been evaluated experimentally.