Connected Components in Undirected Set--Based Graphs. Applications in Object--Oriented Model Manipulation

TL;DR

This paper presents a new algorithm for efficiently finding connected components in set-based graphs, particularly useful in object-oriented model transformations, achieving constant time under specific set restrictions.

Contribution

Introduces a novel constant-time algorithm for connected components in set-based graphs applicable to object-oriented model transformations.

Findings

Algorithm achieves constant computational costs under certain restrictions.

Prototype implementation demonstrates practical effectiveness.

Applicable to transforming connections into equations in object-oriented models.

Abstract

This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the remarkable property of achieving constant computational costs with the number of vertices and edges. The mentioned restrictions are related to the possibility of representing the sets of vertices by intension and the sets of edges using some particular type of maps. While these restrictions can result strong in a general context, they are usually satisfied in the problem of transforming connections into equations in object oriented models, which is the main application of the proposed algorithm. Besides describing the new algorithm and studying its computational cost, the work describes its prototype implementation and shows its application in different examples.