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280
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 418 (21 self)
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is obtained for the 2matching problem and its variants. We also derive the first approximation algorithms for many NPcomplete problems, including the nonfixed pointtopoint connection problem, the exact path partitioning problem, and complex locationdesign problems. Moreover, for the prizecollecting
PRIZECOLLECTING POINT SETS
"... Abstract. Given a set of points P in the plane and profits (or prizes) π: P → R≥0 we want to select a maximum profit set X ⊆ P which maximizes P p∈X π(p) − µ(X) for some particular criterion µ(X). In this paper we consider four such criteria, namely the perimeter and the area of the smallest axisp ..."
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Abstract. Given a set of points P in the plane and profits (or prizes) π: P → R≥0 we want to select a maximum profit set X ⊆ P which maximizes P p∈X π(p) − µ(X) for some particular criterion µ(X). In this paper we consider four such criteria, namely the perimeter and the area of the smallest axisparallel rectangle containing X, and the perimeter and the area of the convex hull conv(X) of X. Our key result is a data structure, called interval heap, that allows us to compute a set of maximum profit with respect to perimeter resp. area of the smallest enclosing axisparallel rectangle in O ` n 2 log n ´ resp. O ` n 3 log n ´ time using O (n) space. In addition, we introduce an O ` n 3 ´ time algorithm for the case that µ(X) measures either the perimeter or the area of conv(X). 1.
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
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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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 polynomial
Combining approximation algorithms for prizecollecting TSP
, 2009
"... We present a 1.91457approximation algorithm for the prizecollecting travelling salesman problem. This is obtained by combining a randomized variant of a rounding algorithm of Bienstock et al. [2] and a primaldual algorithm of Goemans and Williamson [5]. ..."
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Cited by 4 (0 self)
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We present a 1.91457approximation algorithm for the prizecollecting travelling salesman problem. This is obtained by combining a randomized variant of a rounding algorithm of Bienstock et al. [2] and a primaldual algorithm of Goemans and Williamson [5].
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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of bounded treewidth. An analogous hardness result can be shown for Euclidian PCSF. This ends the common belief that prizecollecting variants should not add any new hardness to the problems.
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
Local search with perturbations for the prizecollecting Steiner tree problem in graphs
 Networks
, 2001
"... Abstract. Given an undirected graph with prizes associated with its nodes and weights associated with its edges, the prizecollecting Steiner tree problem consists of finding a subtree of this graph which minimizes the sum of the weights of its edges plus the prizes of the nodes not spanned. In this ..."
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Cited by 51 (26 self)
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Abstract. Given an undirected graph with prizes associated with its nodes and weights associated with its edges, the prizecollecting Steiner tree problem consists of finding a subtree of this graph which minimizes the sum of the weights of its edges plus the prizes of the nodes not spanned
Results 1  10
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280