Finding a minimal transitive reduction in a strongly connected digraph within linear time
This paper describes an algorithm for finding a minimal transitive reduction G red of a given directed graph G, where G red means a subgraph of G with the same transitive closure as G but itself not contains a proper subgraph G1 with the same property too. The algorithm uses depth-first search and two graph transformations preserving the transitive closure to achieve a time bound of O(n + m), where n stands for the number of vertices and m is the number of the edges.
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- S. Even: Graph Algorithms, Computer Science Press, Potomac, MD, 1979.Google Scholar
- D. Harel: A linear time algorithm for finding dominators in flow graphs and related problems, seventeenth annual ACM Symposiumon theory of computing, Providence, 1985, 185–194.Google Scholar
- K. Mehlhorn: Data Structures and Algorithms, Vol. 2: Graph Algorithms and NP-Completeness, Springer, EATCS Monographs in Computer Science, 1984.Google Scholar
- R. Haddad, A. Schäffer: Recognizing Bellman-Ford-Orderable Graphs, Computer Science Department Stanford University, Standford, California 94305-2140.Google Scholar
- K. Simon: On Minimum Flow and Transitive Reduction, Proceedings ICALP'88, Tampere, Lecture Notes in Computer Science, Springer-Verlag, 317, 535–560.Google Scholar