A Survey of Shortest-Path Algorithms
Amgad Madkour, Walid G. Aref, Faizan Ur Rehman, Mohamed Abdur Rahman,, Saleh Basalamah

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.…
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Taxonomy
TopicsOptimization and Search Problems · Complexity and Algorithms in Graphs · Data Management and Algorithms
