Abstract
This paper presents a novel approach called vertical breadth-first tree that utilizes vertical data structures to find all-length paths (including shortest paths) for all pairs of vertices in a graph. Identifying all available paths, including shortest paths is a relevant research problem as this concept can help solve a range of complex problems (e.g., routing problems in computer networks). The advancement of technology, complex computer networks, and extensive exchange of internet communications have resulted in massive increase in data. The conventional path finding algorithms do not scale well with the massive volume of data being communicated over the network and this motivates the need to develop some scalable and efficient path finding algorithms.
Our approach is an advancement of breadth-first algorithm and uses logical operations for path identification. Using vertical data structure, our approach identifies all paths of varying lengths in a graph and stores those paths in the form of a multilevel bit vector tree (MBVT). This MBVT results in faster computation of shortest path from source vertex to target vertex with the use of indexes. Additionally, our proposed algorithm with vertical data structures is more suitable in distributed processing. Our proposed approach allows addition or removal of any edge in the graph without creating the need to re-generate the multilevel bit vector tree. The results of the implementation of our approach on three sample graphs show that vertical breadth-first approach performed shortest path computations compared with existing approaches (Dijkstra’s and all-pair shortest path). The results also show that, when queried about the shortest path between any two vertices, our algorithm just needs to perform a simple look-up in multilevel bit vector tree via indexes which significantly improves the overall efficiency of shortest-path identification.
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Singh, M., Anu, V., Walia, G.S. (2020). A Vertical Breadth-First Multilevel Path Algorithm to Find All Paths in a Graph. In: Alhajj, R., Moshirpour, M., Far, B. (eds) Data Management and Analysis. Studies in Big Data, vol 65. Springer, Cham. https://doi.org/10.1007/978-3-030-32587-9_10
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