Data structures and network algorithms
Data structures and network algorithms
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Shortest path algorithms for nearly acyclic directed graphs
Theoretical Computer Science - Special issue: graph theoretic concepts in computer science
Discrete Applied Mathematics - Special issue: Special issue devoted to the fifth annual international computing and combinatories conference (COCOON'99) Tokyo, Japan 26-28 July 1999
Improved shortest path algorithms for nearly acyclic graphs
Theoretical Computer Science
Efficient algorithms for solving shortest paths on nearly acyclic directed graphs
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
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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 sc-component. 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 1-2-dominator decomposition are dominated by one or two trigger vertices cooperatively. Such subgraphs are potentially larger than those decomposed by the 1-dominator set. Thus fewer trigger vertices are needed to cover the graph.