Abstract
The multipath challenge is a research line in continuous development because of its multiple benefits, however, these benefits are overshadowed by scalability, which goes down considerably when the paths are multiple and disjoint. The disjointness aggregates an extra value to the multiple paths, but it also implies more complex mathematical operations that increase the computational cost. In fact, diverse proposals exist that try to increase scalability by limiting the number of paths obtained to the minimum possible (two-disjoint paths), which is enough for backup applications but not for other purposes. This paper presents an algorithm that solves these drawbacks by discovering multiple disjoint paths among multiple nodes in an efficient way, while keeping bounded the computational cost and ensuring scalability. The proposed algorithm has been validated thoroughly by performing a theoretical analysis, bolstered afterwards by an exhaustive experimental evaluation. The collected results are promising, our algorithm reduces the time spent to obtain the disjoint paths regarding its competitors between one and three orders of magnitude, at the cost of a slight decrease in the number of paths discovered.
Highlights
The shortest path search is a well-known topic in graph theory, being Dijkstra’s algorithm [1] the most renowned solution
EVALUATION This section aims to evaluate the implementation of Multiple Disjoint Path algorithm (MDPAlg) in terms of: (1) computational complexity, with a particular focus on its scalability considering the network size, (2) the number of disjoint paths discovered, and (3) the time needed to obtain all disjoint paths, in direct comparison to Dijkstra’s algorithm
We leveraged Xiaodong Wang’s library [36], available for MATLAB, because it implements Dijkstra’s algorithm based on a matrix of costs, which simplifies the coding process of MDPAlg. This is relevant since the first phase of MDPAlg is inspired by Dijkstra’s algorithm search process, and besides, it computes the cumulative cost from the given node in a cost matrix
Summary
The shortest path search is a well-known topic in graph theory, being Dijkstra’s algorithm [1] the most renowned solution It has been extensively used as the basis for routing protocols in data networks over the last 60 years. D. Lopez-Pajares et al.: Disjoint Multipath Challenge: Multiple Disjoint Paths Guaranteeing Scalability and the remaining nodes in a graph. Lopez-Pajares et al.: Disjoint Multipath Challenge: Multiple Disjoint Paths Guaranteeing Scalability and the remaining nodes in a graph Thereafter, the second phase leverages this extra information to build multiple disjoint paths, avoiding iterative executions when more than one path is required as in Dijkstra and other alike algorithms This methodology keeps the number of mathematical operations bounded, guaranteeing the scalability of the algorithm in large graphs.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
