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A 2.5 Factor Approximation Algorithm for the kMST Problem
 Information Processing Letters
, 1997
"... The kMST problem requires finding that subset of k vertices of a given graph whose Minimum Spanning Tree has least weight amongst all subsets of k vertices. There has been much work on this problem recently, culminating in an approximation algorithm by Garg [G], which finds a subset of k vertices w ..."
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Cited by 19 (0 self)
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whose MST has weight at most 3 times the optimal. Garg also argued that a factor of 3 cannot be improved unless lower bounds different from his are used. We use a pruning technique on top of Garg's algorithm to achieve an approximation factor of 2.5. Note that Garg's algorithm is based upon
A 2+ɛ Approximation Algorithm for the kMST Problem
 IN PROCEEDINGS OF THE 11TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 2000
"... For any ɛ > 0 we give a (2+ɛ)approximation algorithm for the problem of finding a minimum tree spanning any k vertices in a graph (kMST), improving a 3approximation algorithm by Garg [5]. As in [5] the algorithm extends to a (2+ɛ)approximation algorithm for the minimum tour that visits any k ..."
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Cited by 20 (0 self)
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For any ɛ > 0 we give a (2+ɛ)approximation algorithm for the problem of finding a minimum tree spanning any k vertices in a graph (kMST), improving a 3approximation algorithm by Garg [5]. As in [5] the algorithm extends to a (2+ɛ)approximation algorithm for the minimum tour that visits any k
A 2 + ffl approximation algorithm for the kMST problem
"... Abstract For any ffl> 0 we give a (2+ffl)approximation algorithm for the problem of finding a minimum tree spanning any k vertices in a graph (kMST), improving a3approximation algorithm by Garg [5]. As in [5] the algorithm extends to a (2+ffl)approximation algorithmfor the minimum tour that ..."
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Abstract For any ffl> 0 we give a (2+ffl)approximation algorithm for the problem of finding a minimum tree spanning any k vertices in a graph (kMST), improving a3approximation algorithm by Garg [5]. As in [5] the algorithm extends to a (2+ffl)approximation algorithmfor the minimum tour
A constantfactor approximation for the kMST problem in the plane
 In Proceedings of the 27th Annual ACM Symposium on Theorem of Computing (Las Vegas
, 1995
"... We present an algorithm that gives a constant factor approximation for the following problem. Given a set of n points in the plane with a Euclidean distance metric and an integer k < n, find the tree of least weight that spans k points. If desired, one may also specify in the problem a “root vert ..."
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Cited by 30 (5 self)
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We present an algorithm that gives a constant factor approximation for the following problem. Given a set of n points in the plane with a Euclidean distance metric and an integer k < n, find the tree of least weight that spans k points. If desired, one may also specify in the problem a “root
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Guillotine subdivisions approximate polygonal subdivisions: Part II  A simple polynomialtime approximation scheme for geometric kMST, TSP, and related problems
, 1996
"... this paper, thereby achieving essentially the same results that we report here, using decomposition schemes that are somewhat similar to our own. Arora's remarkable results predate this paper by several weeks, and his discovery was done independently of this work. 2 mGuillotine Subdivisions ..."
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Cited by 187 (12 self)
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this paper, thereby achieving essentially the same results that we report here, using decomposition schemes that are somewhat similar to our own. Arora's remarkable results predate this paper by several weeks, and his discovery was done independently of this work. 2 mGuillotine Subdivisions
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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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
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing
Results 1  10
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