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Greedy Algorithms for Steiner Forest
"... In the Steiner Forest problem, we are given terminal pairs {si, ti}, and need to find the cheapest subgraph which connects each of the terminal pairs together. In 1991, Agrawal, Klein, and Ravi, and Goemans and Williamson gave primaldual constantfactor approximation algorithms for this problem; un ..."
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In the Steiner Forest problem, we are given terminal pairs {si, ti}, and need to find the cheapest subgraph which connects each of the terminal pairs together. In 1991, Agrawal, Klein, and Ravi, and Goemans and Williamson gave primaldual constantfactor approximation algorithms for this problem
Approximation Algorithms for Directed Steiner Problems
 Journal of Algorithms
, 1998
"... We give the first nontrivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications in network design and multicast routing. For both problems, the best ratios known before our work we ..."
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Cited by 177 (8 self)
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We give the first nontrivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications in network design and multicast routing. For both problems, the best ratios known before our work
Online Generalized Steiner Problem
, 1996
"... The Generalized Steiner Problem (GSP) is defined as follows. We are given a graph with nonnegative weights and a set of pairs of vertices. The algorithm has to construct minimum weight subgraph such that the two nodes of each pair are connected by a path. Offline generalized Steiner problem ap ..."
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Cited by 51 (5 self)
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approximation algorithms were given in [AKR91, GW92]. We consider the online generalized Steiner problem, in which pairs of vertices arrive online and are needed to be connected immediately. We give a simple O(logĀ² n) competitive deterministic online algorithm. The previous best algorithm was O( p n
Online Steiner Trees in the Euclidean Plane
 Discrete and Computational Geometry
, 1993
"... Suppose we are given a sequence of n points in the Euclidean plane, and our objective is to construct, online, a connected graph that connects all of them, trying to minimize the total sum of lengths of its edges. The points appear one at a time, and at each step the online algorithm must construc ..."
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Cited by 47 (3 self)
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algorithm is measured by its competitive ratio: the supremum, over all sequences of points, of the ratio between the total length of the graph constructed by our algorithm and the total length of the best Steiner tree that connects all the points. There are known online algorithms whose competitive ratio
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 951 (12 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed
The Prize Collecting Steiner Tree Problem
 In Proceedings of the 11th Annual ACMSIAM Symposium on Discrete Algorithms
, 1998
"... This work is motivated by an application in local access network design that can be modeled using the NPhard Prize Collecting Steiner Tree problem. We consider several variants on this problem and on the primaldual 2approximation algorithm devised for it by Goemans and Williamson. We develop seve ..."
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Cited by 103 (1 self)
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This work is motivated by an application in local access network design that can be modeled using the NPhard Prize Collecting Steiner Tree problem. We consider several variants on this problem and on the primaldual 2approximation algorithm devised for it by Goemans and Williamson. We develop
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
 Combinatorica
"... We present a factor 2 approximation algorithm for finding a minimumcost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, which is also known as the survivable network design problem. Our algorit ..."
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Cited by 270 (3 self)
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We present a factor 2 approximation algorithm for finding a minimumcost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, which is also known as the survivable network design problem. Our
Steiner Tree Problems
, 2000
"... this article, we will review important developments in 1990s and discuss some open problems which may induce important developments in this centrary ..."
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Cited by 12 (3 self)
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this article, we will review important developments in 1990s and discuss some open problems which may induce important developments in this centrary
When trees collide: An approximation algorithm for the generalized Steiner problem on networks
, 1994
"... We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair fi; jg of nodes, an edgeconnectivity requirement r ij . The goal is to find a minimumcost network using the a ..."
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Cited by 256 (39 self)
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We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair fi; jg of nodes, an edgeconnectivity requirement r ij . The goal is to find a minimumcost network using
Results 1  10
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44,984