Shortest paths search method based on the projective description of unweighted mixed graphs

TL;DR

This paper introduces a novel shortest path search method for unweighted mixed graphs using refined projections that improve computational efficiency and extend applicability to mixed graph classes.

Contribution

The paper presents a new shortest path search technique based on projective descriptions, reducing complexity and enabling efficient processing of mixed graphs.

Findings

Reduces algorithmic complexity to linear for vertex pairs

Extends shortest path methods to mixed graphs

Improves real-time performance of path searches

Abstract

The method is based on the preliminary transformation of the traditionally used matrices or adjacency lists in the graph theory into refined projections free from redundant information, and their subsequent use in constructing shortest paths. Unlike adjacency matrices and lists based on enumerating binary adjacency relations, the refined projection is based on enumerating more complex relations: simple paths from a given graph vertex that are shortest. The preliminary acquisition of such projections reduces the algorithmic complexity of applications using them and improves their volumetric and real-time characteristics to linear ones for a pair of vertices. The class of graphs considered is extended to mixed graphs.