A. Agrawal, P. Klein and R. Ravi, When trees collide: an approximation algorithm for the generalized Steiner tree problem on networks, SIAM J Computing 24 (1995), 445-456.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....[ f1g stating an upper bound on the number of copies of edge e we are allowed to use; if u e = 1, then there is no bound on the number of copies of edge e. All LP duality based approximation algorithms for the metric Steiner tree problem and its generalizations work with the undirected relaxation [1, 9, 10, 20]. In order to give the integer programming formulation on which this relaxation is based, we will define a cut requirement function f : 2 . For S V , f(S) is defined to be the largest connectivity requirement separated by the cut (S; S) i.e. f(S) maxfr(u; v)ju 2 S and v 2 Sg. Let us ....

A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing, 24(3):440--456, June 1995.

....or may not be included in the solution (Steiner nodes) In instances 1 and 2 a link between non fixed sites has cost 1, a link between a non fixed site and a fixed site has cost 2 and a link between two fixed sites has cost 4. In instance 3 the links have costs randomly selected in the interval [1,200], satisfying the triangular inequality. Network 1 has a double grid structure, with 33 fixed sites, 87 Steiner sites and 286 feasible connections. The objective is to find a 2 node survivable network with minimal cost (all connection requirement between fixed sites are equal to 2) Network 2 ....

A. Agrawal, P. Klein, and R. Ravi, "When trees collide: An approximation algorithm for the Generalized Steiner Problem in Networks" report CS-90-32 (1994), Department of Computer Science, Brown University.

....due to Jain [17] however, this algorithm requires linear programming and is therefore much slower. The WGMV algorithm performs several iterations of the Goemans Williamson clustering procedure [15] a general technique (which builds on an earlier technique due to Agrawal, Klein and Ravi [1]) which forms the core of several algorithms and is described below. Broadly, an iteration will comprise several rounds, in each of which the algorithm will identify some subsets of vertices as active and some as inactive and choose two such subsets to merge into one using an edge addition step. ....

A. Agrawal, P. Klein, R. Ravi. When trees collide: an approximation algorithm for the generalized Steiner problem on networks. Proceedings of the Twenty-third Annual ACM Symposium on Theory of Computing, pp. 134--144, 1991.

....as an independent component at a single location p. Note that since the ghosts grow indefinitely, eventually the set will consist of a single component. We would like to point out a correspondence between the way the set grows and the standard primaldual algorithm for Steiner tree (see [3], and also [15] that will be useful later. The algorithm maintains a list of components. Initially, each terminal vertex is in a separate component. It grows a ball uniformly around every vertex, and whenever the balls of two vertices touch, it builds the edge joining the two vertices, merging ....

....# # can pay for (1 3 of) the rental cost of the network. The next section is devoted to showing that the shares # can pay for a constant fraction of the tree we build. 9 3. 4 Bounding the tree cost For the purposes of analysis we assume that the primal dual algorithm of Agarwal et al. is used [3] (see also [15] to build a Steiner tree on the open centers. The algorithm starts with each center in a separate component. It grows a ball uniformly around every center. Every time two balls touch, a check is performed if the centers of the balls are in the same component. If not, a shortest ....

A. Agrawal, P. Klein, R. Ravi. When Trees Collide: An approximation algorithm for the generalized Steiner Tree problem on networks. SIAM Journal on Computing, 24(3):440-456, 1995.

....constraints. Several fundamental problems fit into this class, e.g. Shortest Path, Minimum Spanning Tree, Minimum Steiner Tree, and generalizations of the Minimum Steiner Tree problems. The above clustering technique was a generalization of the approximation algorithm of Agrawal, Klein and Ravi [1] for the Generalized Steiner Tree problem. Goemans and Williamson [2] originally used this technique to obtain slightly better than 2 approximation factors for several network design problems, including the Generalized Steiner Tree problem, the Non Fixed Point to Point Connection problem, the ....

A. Agrawal, P. Klein, R. Ravi. When trees collide: An approximation algorithm for the generalized steiner problem on networks, SIAM Journal on Computing, 24(3), pp. 440--456, 1995.

....graphs, which is more accurate but slower than a recent algorithm of Cole et.al. 5] 1 Introduction Many approximation algorithms are applications of the primal dual algorithm of Goemans and Williamson (GW) 11] This algorithm is rooted in the approach proposed by Agrawal, Klein and Ravi [2]. This paper determines the asymptotic time complexity of the GW clustering operation on metric spaces. Although our improvement is a sublogarithmic factor, the issue is important from a theoretic viewpoint. Also our algorithm uses simple data structures that will not incur much overhead in a ....

A. Agrawal, P. Klein and R. Ravi, When trees collide: An approximation algorithm for the generalized Steiner problem on networks, SIAM J. Comp. 24, 1995, pp.440--456.

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A. Agrawal, P. Klein and R. Ravi, When trees collide: an approximation algorithm for the generalized Steiner tree problem on networks, SIAM J Computing 24 (1995), 445-456.

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing, 24:440--456, 1995.

....of at most . Thus the total cost of this graph is at most times that of the TSP tour that we started with. This in turn is at most . However, we can apply an approximate min max relation between a MST and a packing of cuts in the graph that is derived in [1, 14] in proving a better performance guarantee for the total cost. In particular, if denotes the cost of a minimum connected subgraph, we show that . This would prove that the cost of the connected subgraph output by our algorithm is as claimed in Theorem 6.2. It remains to prove ....

.... , the sum of the weights of all the cuts in this collection containing the edge is at most . The value of the packing is the sum of the weights of all the cuts in the packing. A maximum packing is one of maximum value. The following theorem is a consequence of the results in [1, 14]. Theorem 6.3 Given an undirected graph with edge weights, a minimum weight spanning tree has weight at most twice the value of a maximum packing of cuts. The algorithms in [1, 14] find a greedy packing of cuts and simultaneously build a minimum spanning tree of weight at most twice the value of ....

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A. Agrawal, P. Klein and R. Ravi, "When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks," SIAM J. Computing, Vol. 24, pp. 440--456, 1995.

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A. Agrawal, P. Klein, R. Ravi. When Trees Collide: An approximation algorithm for the generalized Steiner Tree problem on networks. SIAM Journal on Computing, 24(3):440456, 1995.

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Ajit Agrawal, Philip Klein, and R. Ravi, \When trees collide : An approximation algorithm for the generalized Steiner problem on networks", SIAM Journal on Computing, 24(3) 445-456 (1995).

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing, 24:440--456, 1995.

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing, 24(3):440-456, 1995. Preliminary version in STOC '91.

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A. Agrawal, P. Klein, and R. Ravi, When trees collide: An approximation algorithm for the generalized Steiner problem on networks, in Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, 1991, pp. 134--144. To appear in SIAM J. Comput.

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing, 24(3):440--456, 1995.

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: an approximation algorithm for the generalized Steiner problem on networks. SIAM J. Comput., 24(3):440--456, 1995.

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Ajit Agrawal, Philip Klein, and R. Ravi. When trees collide: an approximation algorithm for the generalized Steiner problem on networks. SIAM J. Comput., 24(3):440--456, 1995.

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM J. on Computing, 24:440-456, 1995.

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for generalized Steiner tree problems on networks. In Proceedings of the 23rd ACM Symposium on Theory of Computing, pages 134--144, 1991.

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing, 24:440--456, 1995.

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing, 24:440--456, 1995.

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing, 24(3) 445-456 (1995).

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing, 24(3):440-- 456, 1995.

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A. Agrawal, P. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM J. on Computing, 24:440456, 1995.

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Ajit Agrawal, Philip Klein, and R. Ravi. When trees collide: an approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing, 24(3):440--456, June 1995.

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