Abstract
We introduce a new problem that combines the well known All Pairs Shortest Paths (APSP) problem and the All Pairs Bottleneck Paths (APBP) problem to compute the shortest paths for all pairs of vertices for all possible flow amounts. We call this new problem the All Pairs Shortest Paths for All Flows (APSP-AF) problem. We firstly solve the APSP-AF problem on directed graphs with unit edge costs and real edge capacities in O(√ tn (ω+9)/4)=O (√ tn2.843) time, where n is the number of vertices, t is the number of distinct edge capacities (flow amounts) and O(nω)
Cite
CITATION STYLE
Shinn, T. W., & Takaoka, T. (2014). Combining all pairs shortest paths and all pairs bottleneck paths problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8392 LNCS, pp. 226–237). Springer Verlag. https://doi.org/10.1007/978-3-642-54423-1_20
Register to see more suggestions
Mendeley helps you to discover research relevant for your work.
