Lawrence Yelowitz
Abstract
The row-oriented algorithm in [1] for obtaining transitive closure is Dijkstra's algorithm [2] (for obtaining all nodes reachable from a single node) applied to each row in turn. Furthermore, [1] does not work properly in the acyclic case unless the matrix is in triangular form initially. In general, it may be necessary to renumber the nodes (and correspondingly rearrange the matrix) to bring an acyclic adjacency matrix into triangular form (a technique such as topological sorting [3] can be used). Finally, if interest is in obtaining the nonredundant digraph of an acyclic digraph, [4] appears to be a more efficient algorithm than [5].
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Digital Library
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- Knuth, D. E., The Art of Computer Programming, Vol. 1, Fundamental Algorithms, 2nd Ed., Addison-Wesley Publishing Co., Reading, Mass., 1973. Google ScholarDigital Library
- Yelowitz, L., An efficient algorithm for constructing hierarchical graphs, IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-6, No. 4, April 1976, pp. 327--329.Google ScholarCross Ref
- Shyamasundar, R. K., and Krishnamurthy, E. V., Algorithms for constructing hierarchical graphs, IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-4, 1974, pp. 459--461.Google ScholarCross Ref
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- Notes on "A note on the transitive closure of a boolean matrix"
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