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Approximation schemes for nodeweighted geometric Steiner tree problems
"... Abstract. In this paper we introduce a new technique for approximation schemes for geometrical optimization problems. As an example problem, we consider the following variant of the geometric Steiner tree problem. Every point u which is not included in the tree costs a penalty of pi(u) units. Furth ..."
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Abstract. In this paper we introduce a new technique for approximation schemes for geometrical optimization problems. As an example problem, we consider the following variant of the geometric Steiner tree problem. Every point u which is not included in the tree costs a penalty of pi(u) units
NodeWeighted Prize Collecting Steiner Tree and Applications
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii The Steiner Tree problem has appeared in the Karp’s li ..."
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list of the first 21 NPhard problems and is well known as one of the most fundamental problems in Network Design area. We study the NodeWeighted version of the Prize Collecting Steiner Tree problem. In this problem, we are given a simple graph with a cost and penalty value associated with each node
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
Online Nodeweighted Steiner . . .
"... We obtain the first online algorithms for the nodeweighted Steiner tree, Steiner forest and group Steiner tree problems that achieve a polylogarithmic competitive ratio. Our algorithm for the Steiner tree problem runs in polynomial time, while those for the other two problems take quasipolynomia ..."
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We obtain the first online algorithms for the nodeweighted Steiner tree, Steiner forest and group Steiner tree problems that achieve a polylogarithmic competitive ratio. Our algorithm for the Steiner tree problem runs in polynomial time, while those for the other two problems take quasi
A nearly bestpossible approximation algorithm for nodeweighted Steiner trees
, 1993
"... We give the first approximation algorithm for the nodeweighted Steiner tree problem. Its performance guarantee is within a constant factor of the best possible unless ~ P ' NP . Our algorithm generalizes to handle other network design problems. ..."
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Cited by 138 (10 self)
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We give the first approximation algorithm for the nodeweighted Steiner tree problem. Its performance guarantee is within a constant factor of the best possible unless ~ P ' NP . Our algorithm generalizes to handle other network design problems.
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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in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include
Approximating nodeweighted multicast trees in wireless adhoc networks
 In Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing: Connecting the World Wirelessly (IWCMC 2009
, 2009
"... Multicast communication in a wireless adhoc network can be established using a tree that spans the multicast sender and receivers as well as other intermediate nodes. If the network is modelled as a graph, the multicast tree is a Steiner tree, the multicast sender and receivers correspond to term ..."
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Cited by 3 (2 self)
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the problem of computing, for a given nodeweighted graph and a set of terminals, a Steiner tree with Steiner nodes of minimum total weight. For graph classes that admit spanning trees of maximum degree at most d, we obtain a 0.775dapproximation algorithm. We show that this result implies a 3
Approximations for nodeweighted Steiner tree in unit disk graphs
 OPTIM LETT
, 2009
"... Given a nodeweighted connected graph and a subset of terminals, the problem nodeweighted Steiner tree (NWST) seeks a lightest tree connecting a given set of terminals in a nodeweighted graph. While NWST in general graphs are as hard as Set Cover, NWST restricted to unitdisk graphs (UDGs) admits ..."
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Given a nodeweighted connected graph and a subset of terminals, the problem nodeweighted Steiner tree (NWST) seeks a lightest tree connecting a given set of terminals in a nodeweighted graph. While NWST in general graphs are as hard as Set Cover, NWST restricted to unitdisk graphs (UDGs
Scalable Recognition with a Vocabulary Tree
 IN CVPR
, 2006
"... A recognition scheme that scales efficiently to a large number of objects is presented. The efficiency and quality is exhibited in a live demonstration that recognizes CDcovers from a database of 40000 images of popular music CD's. The scheme ..."
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Cited by 1043 (0 self)
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A recognition scheme that scales efficiently to a large number of objects is presented. The efficiency and quality is exhibited in a live demonstration that recognizes CDcovers from a database of 40000 images of popular music CD's. The scheme
Results 1  10
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