On the quick search for the shortest paths in an unweighted dynamic graph by its projections in brief

TL;DR

This paper introduces a novel method for representing projections of unweighted dynamic graphs in computer memory, enabling quick shortest path searches with low spatial and temporal complexity, suitable for real-time network routing.

Contribution

It proposes a new graph projection representation and a fast shortest path search method specifically designed for unweighted dynamic graphs.

Findings

Spatial complexity does not exceed (d+1)×n words.

Shortest path search takes at most d steps.

Applicable in time delay-critical network routing.

Abstract

For the first time proposed: a method for representing the projections of a graph in computer memory and a description based on it of a quick search for shortest paths in unweighted dynamic graphs. The spatial complexity of the projection description does not exceed $(d + 1)\times n$ words, where $d$ is the diameter and $n$ is the number of vertices of the graph. The temporal difficulty of finding one shortest path between two vertices does not exceed d steps with the duration of elementary time of sampling a machine word. The solution can be applied in time delay-critical routing protocols of computer networks and supercomputers.