D. M. Moyles and G. L. Thompson, An algorithm for finding the minimum equivalent graph of a digraph, Journal of the ACM, 16 (3), pp. 455--460, (1969).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....These results provide practical approximation algorithms for NP hard network design problems via an increased understanding of connectivity properties. Until now, the techniques developed have been applicable only to undirected graphs. We consider a basic network design problem in directed graphs [2, 12, 13, 18] which is as follows: given a digraph, find a smallest subset of the edges (forming a minimum equivalent graph (MEG) that maintains all reachability relations of the original graph. When the MEG problem is restricted to strongly connected graphs we call it the minimum SCSS (strongly connected ....

....given by the socalled strong component graph , together with one minimumSCSS problem for each strong component (given by the subgraph induced by that component) Furthermore, approximating the MEG problem is linear time equivalent to approximating both restricted versions. Moyles and Thompson [18] observe this decomposition and give exponential time algorithms for the restricted problems. Hsu [13] gives a polynomial time algorithm for the acyclic MEG problem. The related problem of finding a transitive reduction of a digraph a smallest set of edges yielding the same reachability ....

D. M. Moyles and G. L. Thompson, An algorithm for finding the minimum equivalent graph of a digraph, Journal of the ACM, 16 (3), pp. 455--460, (1969).

....from u to v using only edges in S. The problem is NP hard [3] A c approximate solution is a subset of edges providing the necessary paths of size at most c times the minimum. A c approximation algorithm is a polynomial time algorithm guaranteeing a c approximate solution. Moyles and Thompson [8] observed that any solution to the MEG problem decomposes into solutions for each strongly connected component and a solution for the component graph (the graph obtained by contracting each strongly connected component) Thus, the problem reduces in linear time to two cases: the graph is either ....

....problem in undirected graphs is to find a minimum size subset of edges preserving 2 edge connectivity. This problem (and many others that are NP hard in general) can be solved optimally in polynomial time for graphs with bounded cycle length [2] 2 Other related work: Moyles and Thompson [8] gave an exponential time algorithm for the MEG problem; Hsu [5] gave a polynomial time algorithm for the acyclic case. Contents: The body of the paper is organized as follows. Section 2 contains the reduction of SCSS 3 to Edge Cover (proving Theorem 1.1) Section 3 notes that Edge Cover reduces ....

D. M. Moyles and G. L. Thompson, An algorithm for finding the minimum equivalent graph of a digraph, Journal of the ACM, 16 (3), pp. 455--460, (1969).

....Furthermore, the reduction preserves approximation, in the sense that c approximate solutions to the subproblems yield a c approximate solution to the original problem. Hence an approximation algorithm for the SCSS problem implies an approximation algorithm for the MEG problem. Moyles and Thompson [31] observe this decomposition and give exponential time algorithms for the restricted problems. Hsu [21] gives a polynomial time algorithm for the acyclic MEG problem. First we describe the basic algorithm that achieves a factor of 1:64 in polynomial time. The algorithm and its analysis are based on ....

D. M. Moyles and G. L. Thompson, An algorithm for finding the minimum equivalent graph of a digraph, Journal of the ACM, 16 (3), pp. 455--460, (1969).

....These results provide practical approximation algorithms for NP hard network design problems via an increased understanding of connectivity properties. Until now, the techniques developed have been applicable only to undirected graphs. We consider a basic network design problem in directed graphs [2, 12, 13, 18] which is as follows: given a digraph, find a smallest subset of the edges (forming a minimum equivalent graph (MEG) that maintains all reachability relations of the original graph. When the MEG problem is restricted to strongly connected graphs we call it the minimum SCSS (strongly connected ....

....with one minimum SCSS problem for each strong component (given by the subgraph induced by that component) Furthermore, the reduction preserves approximation, in the sense that c approximate solutions to the subproblems yield a c approximate solution to the original problem. Moyles and Thompson [18] observe this decomposition and give exponential time algorithms for the restricted problems. Hsu [13] gives a polynomial time algorithm for the acyclic MEG problem. The related problem of finding a transitive reduction of a digraph a smallest set of edges yielding the same reachability ....

D. M. Moyles and G. L. Thompson, An algorithm for finding the minimum equivalent graph of a digraph, Journal of the ACM, 16 (3), pp. 455--460, (1969).

....y Department of Computer Science, The University of Texas at Dallas, Box 830688, Richardson, TX 75083. E mail : rbk utdallas.edu. z Department of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14850. E mail : ney orie.cornell.edu. Moyles and Thompson [8] observe this decomposition and give exponential time algorithms for the restricted problems. Hsu [5] gives a polynomial time algorithm for the acyclic MEG problem. For acyclic graphs, the MEG problem is equivalent to the transitive reduction problem, which is shown by Aho, Garey and Ullman to be ....

D. M. Moyles and G. L. Thompson, An algorithm for finding the minimum equivalent graph of a digraph, Journal of the ACM, 16 (3), pp. 455--460, (1969).

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