Shortest Path Algorithms between Theory and Practice

05/17/2019
by   Ahmed Shokry, et al.
0

Utilizing graph algorithms is a common activity in computer science. Algorithms that perform computations on large graphs are not always efficient. This work investigates the Single-Source Shortest Path (SSSP) problem, which is considered to be one of the most important and most studied graph problems. This thesis contains a review of the SSSP problem in both theory and practice. In addition, it discusses a new single-source shortest-path algorithm that achieves the same O(n · m) time bound as the traditional Bellman-Ford-Moore algorithm but outperforms it and other state-of-the-art algorithms in practice. The work is comprised of three parts. The first discusses some basic shortest-path and negative-cycle-detection algorithms in literature from the theoretical and practical point of view. The second contains a discussion of a new algorithm for the single-source shortest-path problem that outperforms most state-of-the-art algorithms for several well-known families of graphs. The main idea behind the proposed algorithm is to select the fewest most-effective vertices to scan. We also propose a discussion of correctness, termination, and the proof of the worst-case time bound of the proposed algorithm. This section also suggests two different implementations for the proposed algorithm, the first runs faster while the second performs a fewer number of operations. Finally, an extensive computational study of the different shortest paths algorithms is conducted. The results are proposed using a new evaluation metric for shortest-path algorithms. A discussion of outcomes, strengths, and weaknesses of the various shortest path algorithms are also included in this work.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset