D. Gries, A. J. Martin, J. L. A. van de Shepscheut, and J. T. Udding. An algorithm for transitive reduction of an acyclic graph. Science of Computer Programming, 12, 1989, pages 151--155.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....minimal edges. There are two approaches to build a non redundant DDG. The first is a reduction based approach, in which a DDG is built first, and a transitive reduction algorithm can then be used to eliminate redundancies [27] It has shown that the time complexity of this approach is O(n 3 ) [5, 55]. The second is a direct approach in which a non redundant DDG is built directly. In our case, since we our graph is a DAG, better algorithms can be designed if we can take advantage of the leveldirected graph representation. The two algorithms that we will introduce are based on the direct ....

David Gries, Alain J. Martin, Jan L. A. van de Snepscheut, and Jan Tijmen Udding. An algorithm for transitive reduction of an acyclic graph. Science of Computer Programming, 12(2):151--155, July 1989.

....2 1 Introduction Some points: a) What is transitive reduction (b) Why do we need that (e.g. lub and glb in AI applications, and as an opposite extreme of transitive closure) c) Dynamic maintain of transitive reduced graph. d) Previous work in transitive reduction, e.g. [1, 3, 4, 5]. some of them work only for special cases, like strong connected) Given a finite or infinite set U in which a partial ordering # is defined. Let V be a finite subset of U. According to the relation #, assume that a directed acyclic graph (dag) G = V, E) is given and furthermore G is ....

GRIES AND MARTIN AND VAN DE SNEPSCHEUT AND UDDING. An Algorithm for Transitive Reduction of an Acyclic Graph. Science of Computer Programming 12(2), 1989

....each dependency arc. The minimal synchronization problem (msp) can be formalized as shown in Definition 1. The required synchronizations will be a subset of A, the set of dependency arcs. The problem under consideration is closely related to the transitive closure and transitive reduction problems [2, 3, 4, 7]. Our work is distinct from Shaffer s work in two respects: ffl We consider eliminating dependencies before and after scheduling. In our simulations (see Section 4) on the average, 98.28 of the dependencies are eliminated before scheduling. This can have a dramatic impact on the efficiency of ....

....for solving MSP is presented. Simulation data is detailed in Section 4 and conclusions are drawn. 2 Transitive Closure and Transitive Reduction The transitive closure of a directed graph (or digraph) G, denoted by G , is obtained by adding an arc (i; j) if there is a path from i to j in G [4, 7]. The transitive closure of a graph indicates the reachability of all pairs of vertices in a graph. Two graphs G and G 0 are said to be transitively equivalent if they have the same transitive closure. Such graphs have the interesting property that a schedule satisfying the precedence relations ....

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D. Gries, A. J. Martin, J. L. A. van de Snepscheut, and J. T. Udding. An algorithm for transitive reduction of an acyclic graph. Science of Computer Programming, 12:151--155, 1989.

....hc and vc are in bit matrix form. For LB1, the HCG and hc need to be updated whenever an edge is added. As the time required for computing the labels h i , h 0 i , lb i and lb 0 i is proportional to the number of arcs in the VCG, we compute the transitive closure and transitive reduction [4, 12] before the VCG is constructed. 6 CONCLUSION In this paper, we have presented two efficient algorithms, LB2 and LB3, for computing a tighter lower bound for the channel routing problem. Algorithm LB2 is based on partitioning and labeling a directed acyclic graph. Algorithm LB3 improves LB2 by ....

D. Gries, A. J. Martin, Jan L. A van de Snepscheut, and J. T. Udding. An algorithm for transitive reduction of an acyclic graph. Science of Computer Programming, 12:151--155, 1989.

.... constraints (e.g. the pipeline scheduling problems [5, 15] superscalar pipeline scheduling problems [8] microcode compaction problems [30] and channel routing problems [32] The problem under consideration is closely related to the transitive closure and transitive reduction problems [2, 4, 10, 12, 14, 26]. In Section 2, we develope a new algorithm which computes the transitive closure and transitive reduction of a DAG simultaneously. In Section 3, we introduce a new algorithm for solving the minimal synchronization problem. The experimental results are shown in Section 4, and conclusions are drawn ....

....problem. The experimental results are shown in Section 4, and conclusions are drawn in Section 5. 2 Transitive Closure and Transitive Reduction The transitive closure, denoted by G , of a directed graph (or digraph) G is obtained by adding an arc (i; j) if there is a path from i to j in G [4, 10, 14, 26]. The transitive closure of a graph indicates the reachability of all pairs of vertices in a graph. Two graphs G and G 0 are said to be transitively equivalent if they have the same transitive closure. Such graphs have the interesting property that a schedule satisfying the precedence relations ....

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D. Gries, A. J. Martin, Jan L. A van de Snepscheut, and J. T. Udding. An algorithm for transitive reduction of an acyclic graph. Science of Computer Programming, 12:151--155, 1989.

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D. Gries, A. J. Martin, J. L. A. van de Shepscheut, and J. T. Udding. An algorithm for transitive reduction of an acyclic graph. Science of Computer Programming, 12, 1989, pages 151--155.

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