Improved Shortest Path Algorithms For Nearly Acyclic Directed Graphs

This paper presents new algorithms for computing single source shortest paths (SSSPs) in a nearly acyclic directed graph G. The first part introduces higher-order decomposition. This decomposition is an extension of the technique of strongly connected component (sc-component) decomposition. The second part presents a new method for measuring acyclicity based on modifications to two existing methods. In the new method, we decompose the graph into a 1-dominator set, which is a set of acyclic subgraphs where each subgraph is dominated by one trigger vertex. Meanwhile we compute sc-components of a degenerated graph derived from triggers. Using this preprocessing, a new SSSP algorithm has O(m + rlogl) time complexity, where r is the size of the 1-dominator set, and l is the size of the largest sccomponent. In the third part, we modify the concept of a 1-dominator set to that of a 1-2-dominator set. Each of acyclic subgraphs obtained by the 12-dominator decomposition are dominated by one ...

• Type: Conference
• Year: 2007
• Where: ACSC
• Authors: Lin Tian, Tadao Takaoka
• Keywords: 1-dominator Set, ACSC 2007, Acyclic Directed Graph, Acyclic Subgraphs, Computer Science