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The PrizeCollecting Generalized Steiner Tree Problem Via A New Approach Of PrimalDual Schema
"... In this paper we study the prizecollecting version of the Generalized Steiner Tree problem. To the best of our knowledge, there is no general combinatorial technique in approximation algorithms developed to study the prizecollecting versions of various problems. These problems are studied on a cas ..."
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Cited by 47 (15 self)
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). We fuse the primaldual schema with Farkas lemma to obtain a combinatorial 3approximation algorithm for the PrizeCollecting Generalized Steiner Tree problem. Our work also inspires a combinatorial algorithm [12] for solving a special case of Kelly’s problem [21] of pricing edges. We also consider
PrizeCollecting Steiner Network Problems
"... In the Steiner Network problem we are given a graph G with edgecosts and connectivity requirements ruv between node pairs u, v. The goal is to find a minimumcost subgraph H of G that contains ruv edgedisjoint paths for all u, v ∈ V. In PrizeCollecting Steiner Network problems we do not need to ..."
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Cited by 8 (6 self)
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In the Steiner Network problem we are given a graph G with edgecosts and connectivity requirements ruv between node pairs u, v. The goal is to find a minimumcost subgraph H of G that contains ruv edgedisjoint paths for all u, v ∈ V. In PrizeCollecting Steiner Network problems we do not need
Primaldual approximation algorithms for the PrizeCollecting Steiner Tree Problem
 Information Processing Letters
"... The primaldual scheme has been used to provide approximation algorithms for many problems. Goemans and Williamson gave a (2 − 1 n−1)approximation for the PrizeCollecting Steiner Tree Problem that runs in O(n3 logn) time. Their algorithm applies the primaldual scheme once for each of the n vertic ..."
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Cited by 6 (2 self)
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The primaldual scheme has been used to provide approximation algorithms for many problems. Goemans and Williamson gave a (2 − 1 n−1)approximation for the PrizeCollecting Steiner Tree Problem that runs in O(n3 logn) time. Their algorithm applies the primaldual scheme once for each of the n
Euclidean Prizecollecting Steiner Forest
, 2009
"... In this paper, we consider Steiner forest and its generalizations, prizecollecting Steiner forest and kSteiner forest, when the vertices of the input graph are points in the Euclidean plane and the lengths are Euclidean distances. First, we present a simpler analysis of the polynomialtime approxi ..."
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Cited by 5 (4 self)
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.e., the multiplicative case, of prizecollecting and budgeted Steiner forest. The ideas used in the algorithm may have applications in design of a broad class of bicriteria PTASs. At the end, we demonstrate why PTASs for these problems can be hard in the general Euclidean case (and thus for PTASs we cannot go beyond
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
Prizecollecting Steiner networks via iterative rounding
 in Proceedings of The 9th Latin American Theoretical Informatics Symposium (LATIN
, 2010
"... Abstract. In this paper we design an iterative rounding approach for the classic prizecollecting Steiner forest problem and more generally the prizecollecting survivable Steiner network design problem. We show as an structural result that in each iteration of our algorithm there is an LP variable ..."
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Cited by 6 (1 self)
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Abstract. In this paper we design an iterative rounding approach for the classic prizecollecting Steiner forest problem and more generally the prizecollecting survivable Steiner network design problem. We show as an structural result that in each iteration of our algorithm there is an LP variable
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
PRIMAL AND DUAL BOUNDS FOR THE PRIZECOLLECTING STEINER PROBLEM IN GRAPHS
"... ABSTRACT. Given an undirected graph G with associated edge costs and vertex penalties, a Prize Collecting Steiner (PCS) tree is either an isolated vertex of G or else any tree of that graph. The weight of a PCS tree equals the sum of its edge costs plus the sum of the penalties for the vertices of G ..."
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of G not spanned by the tree. The Prize Collecting Steiner Problem in Graphs (PCSPG) is to find a PCS tree of lowest weight. In this paper, we introduce Lagrangian Non Delayed Relax and Cut (NDRC) and Linear Programming based algorithms to generate primal and dual bounds to PCSPG. The algorithms
Solving the prizecollecting Steiner tree problem to optimality
 PROCEEDINGS OF ALENEX, SEVENTH WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS
, 2005
"... The PrizeCollecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears in the design of utility networks (eg. f ..."
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Cited by 8 (1 self)
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The PrizeCollecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears in the design of utility networks (eg
Results 1  10
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