Search for shortest paths based on a projective description of unweighted graphs

TL;DR

This paper introduces a novel method for shortest path search in unweighted graphs using projective transformations of adjacency data, applicable to mixed graphs, reducing complexity for various practical network applications.

Contribution

It proposes a new projection-based approach for shortest path search in mixed graphs, expanding the class of graphs and improving algorithmic efficiency.

Findings

Reduced algorithmic complexity demonstrated

Applicable to mixed graphs with undirected and directed edges

Potential for use in diverse network-related fields

Abstract

The search is based on the preliminary transformation of matrices or adjacency lists traditionally used in the study of graphs into projections cleared of redundant information (refined) followed by the selection of the desired shortest paths. Each projection contains complete information about all the shortest paths from its base (angle vertex) and is based on an enumeration of reachability relations, more complex than the traditionally used binary adjacency relations. The class of graphs considered was expanded to mixed graphs containing both undirected and oriented edges (arcs). A method for representing graph projections in computer memory and finding shortest paths using them is proposed. The reduction in algorithmic complexity achieved, at the same time, will allow the proposed method to be used in information network applications, scientific and technical, transport and logistics, and economic fields.