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754
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
 In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science (FOCS’96
, 1996
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes a ..."
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Cited by 399 (3 self)
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to Christofides) achieves a 3/2approximation in polynomial time. We also give similar approximation schemes for some other NPhard Euclidean problems: Minimum Steiner Tree, kTSP, and kMST. (The running times of the algorithm for kTSP and kMST involve an additional multiplicative factor k.) The previous best
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
Improved Approximation Algorithms for PRIZECOLLECTING STEINER TREE and TSP
"... Abstract — We study the prizecollecting versions of the Steiner tree, traveling salesman, and stroll (a.k.a. PATHTSP) problems (PCST, PCTSP, and PCS, respectively): given a graph (V, E) with costs on each edge and a penalty (a.k.a. prize) on each node, the goal is to find a tree (for PCST), cycle ..."
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Cited by 32 (6 self)
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Abstract — We study the prizecollecting versions of the Steiner tree, traveling salesman, and stroll (a.k.a. PATHTSP) problems (PCST, PCTSP, and PCS, respectively): given a graph (V, E) with costs on each edge and a penalty (a.k.a. prize) on each node, the goal is to find a tree (for PCST), cycle
Prizecollecting Steiner Problems on Planar Graphs
"... In this paper, we reduce PrizeCollecting Steiner TSP (PCTSP), PrizeCollecting Stroll (PCS), PrizeCollecting Steiner Tree (PCST), PrizeCollecting Steiner Forest (PCSF), and more generally Submodular PrizeCollecting Steiner Forest (SPCSF), on planar graphs (and also on boundedgenus graphs) to the ..."
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Cited by 9 (2 self)
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In this paper, we reduce PrizeCollecting Steiner TSP (PCTSP), PrizeCollecting Stroll (PCS), PrizeCollecting Steiner Tree (PCST), PrizeCollecting Steiner Forest (PCSF), and more generally Submodular PrizeCollecting Steiner Forest (SPCSF), on planar graphs (and also on boundedgenus graphs
Universal approximations for TSP, Steiner tree, and set cover
 In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC’05
, 2005
"... We introduce a notion of universality in the context of optimization problems with partial information. Universality is a framework for dealing with uncertainty by guaranteeing a certain quality of goodness for all possible completions of the partial information set. Universal variants of optimizati ..."
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Cited by 36 (3 self)
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of optimization problems can be defined that are both natural and wellmotivated. We consider universal versions of three classical problems: TSP, Steiner Tree and Set Cover. We present a polynomialtime algorithm to find a universal tour on a given metric space over vertices such that for any subset
Dynamic Steiner Tree and Subgraph TSP
"... In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an nvertex graph G = (V,E,w) with positive real edge weights, and our goal is to maintain a tree inG which is a good approximation of the minimum Steiner tree spanning a termina ..."
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In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an nvertex graph G = (V,E,w) with positive real edge weights, and our goal is to maintain a tree inG which is a good approximation of the minimum Steiner tree spanning a
2 STEINER TREE PROBLEM
, 2011
"... We study the Primal Dual approach in approximation algorithms for the NP hard problems of: Steiner tree problem andPrize collecting steiner tree problem. ..."
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We study the Primal Dual approach in approximation algorithms for the NP hard problems of: Steiner tree problem andPrize collecting steiner tree problem.
A polylogarithmic approximation algorithm for the group Steiner tree problem
 Journal of Algorithms
, 2000
"... The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich a ..."
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Cited by 150 (9 self)
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The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich
Results 1  10
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754