Abstract
Abuaiadh and Kingston gave an efficient algorithm for the single source shortest path problem for a nearly acyclic graph with O(m+ n log t) computing time, where m and n are the numbers of edges and vertices of the given directed graph and t is the number of delete-min operations in the priority queue manipulation. They use the Fibonacci heap for the priority queue. If the graph is acyclic, we have t=0 and the time complexity becomes O(m+n) which is linear and optimal. They claim that if the graph is nearly acyclic, t is expected to be small and the algorithm runs fast. In the present paper, we take another definition of acyclicity. The degree of cyclicity cyc(G) of graph G is defined by the maximum cardinality of the strongly connected components of G. When cyc(G)=k is small, we can say the graph is nearly acyclic and we give an algorithm for the single source problem with O(m+n log k) time complexity. Finally we give a hybrid algorithm that incorporates the merits of the above two algorithms.
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© 1997 Springer-Verlag Berlin Heidelberg
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Takaoka, T. (1997). Shortest path algorithms for nearly acyclic directed graphs. In: d'Amore, F., Franciosa, P.G., Marchetti-Spaccamela, A. (eds) Graph-Theoretic Concepts in Computer Science. WG 1996. Lecture Notes in Computer Science, vol 1197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62559-3_29
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DOI: https://doi.org/10.1007/3-540-62559-3_29
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