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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
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 the Minimum Latency Problem via PrizeCollecting Strolls
"... The minimum latency problem (MLP) is a wellstudied variant of the traveling salesman problem (TSP). In the MLP, the server’s goal is to minimize the average latency that the clients experience prior to being served, rather than the total latency experienced by the server (as in the TSP). The MLP so ..."
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Cited by 4 (0 self)
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(Chaudhuri et al., 2003). In this paper, we improve the approximation ratio for trees to 3.03. In fact, our 3.03approximation algorithm works for any class of graphs in which the related prizecollecting stroll (PCS) problem is solvable in polynomial time, such as graphs of constant treewidth. More
A Technique for Improving Approximation Algorithms for PrizeCollecting Problems
, 2008
"... We study the prizecollecting versions of the Steiner tree (PCST) and traveling salesman (PCTSP) problems: given a graph (V, E) with costs on each edge and a penalty on each node, the goal is to find a tree (for PCST) or cycle (for PCTSP), that minimizes the sum of the edge costs in the tree/cycle a ..."
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Cited by 1 (1 self)
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We study the prizecollecting versions of the Steiner tree (PCST) and traveling salesman (PCTSP) problems: given a graph (V, E) with costs on each edge and a penalty on each node, the goal is to find a tree (for PCST) or cycle (for PCTSP), that minimizes the sum of the edge costs in the tree
Prizecollecting Network Design on Planar Graphs
, 2010
"... 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 more generally boundedgenus graphs) ..."
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Cited by 6 (4 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 more generally boundedgenus graphs
New Approximation Guarantees for MinimumWeight kTrees and PrizeCollecting Salesmen
, 1999
"... We consider a formalization of the following problem. A salesperson must sell some quota of brushes in order to win a trip to Hawaii. This salesperson has a map (a weighted graph) in which each city has an attached demand specifying the number of brushes that can be sold in that city. What is the be ..."
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Cited by 31 (1 self)
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? In this paper we give the first approximation algorithm having a polylogarithmic performance guarantee for this problem, as well as for the slightly more general "Prize Collecting Traveling Salesman Problem" (PCTSP) of Balas, and a variation we call the "Bankrobber Problem" (also called
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
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 822 (39 self)
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vertex cover, maximum satisfiability, maximum cut, metric TSP, Steiner trees and shortest superstring. We also improve upon the clique hardness results of Feige, Goldwasser, Lovász, Safra and Szegedy [42], and Arora and Safra [6] and shows that there exists a positive ɛ such that approximating
Results 1  10
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7,428