A Survey of Shortest-Path Algorithms

TL;DR

This survey comprehensively classifies and discusses various shortest-path algorithms across different problem variants, graph types, and solution approaches, highlighting challenges and solutions in the field.

Contribution

It introduces a new taxonomy for classifying shortest-path algorithms and provides an organized overview of existing methods and their challenges.

Findings

Classifies shortest-path algorithms based on problem variants and graph dynamics.

Identifies key challenges and solutions for different algorithm categories.

Highlights the lack of a universal algorithm for all shortest-path problem variants.

Abstract

A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of shortest-path algorithms based on a taxonomy that is introduced in the paper. One dimension of this taxonomy is the various flavors of the shortest-path problem. There is no one general algorithm that is capable of solving all variants of the shortest-path problem due to the space and time complexities associated with each algorithm. Other important dimensions of the taxonomy include whether the shortest-path algorithm operates over a static or a dynamic graph, whether the shortest-path algorithm produces exact or approximate answers, and whether the objective of the shortest-path algorithm is to achieve time-dependence or is to only be goal directed. This survey studies and classifies shortest-path algorithms according to the proposed taxonomy. The survey also presents the challenges and proposed solutions associated with each category in the taxonomy.