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449
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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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 NearLinear Time εApproximation Algorithm for Bipartite Geometric Matching
, 2011
"... For point sets A, B ∈ R d, A  = B  = n, and for a parameter ε> 0, we present an algorithm that computes, in O(npoly(log n, 1/ε)) time, a matching whose cost is within (1 + ε) of optimal perfect matching with high probability; the previously best known algorithm takes Ω(n 3/2) time. We appro ..."
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Cited by 2 (0 self)
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For point sets A, B ∈ R d, A  = B  = n, and for a parameter ε> 0, we present an algorithm that computes, in O(npoly(log n, 1/ε)) time, a matching whose cost is within (1 + ε) of optimal perfect matching with high probability; the previously best known algorithm takes Ω(n 3/2) time. We
RUSPACE(log n) \subseteq DSPACE(log² n/log log n)
 THE 7TH ANNUAL INTERNATIONAL SYMPOSIUM ON ALGORITHMS AND COMPUTATION (ISAAC’96
, 1998
"... We present a deterministic algorithm running in space O , log n= log log n # solving the connectivity problem on strongly unambiguous graphs. In addition, we presentanO#log n# timebounded algorithm for this problem running on a parallel pointer machine. ..."
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We present a deterministic algorithm running in space O , log n= log log n # solving the connectivity problem on strongly unambiguous graphs. In addition, we presentanO#log n# timebounded algorithm for this problem running on a parallel pointer machine.
Simple PCPs with Polylog Rate and Query Complexity
, 2005
"... We give constructions of probabilistically checkable proofs (PCPs) of length n·poly(log n) (to prove satisfiability of circuits of size n) that can verified by querying poly(log n) bits of the proof. We also give constructions of locally testable codes (LTCs) with similar parameters. Previous constr ..."
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Cited by 46 (10 self)
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We give constructions of probabilistically checkable proofs (PCPs) of length n·poly(log n) (to prove satisfiability of circuits of size n) that can verified by querying poly(log n) bits of the proof. We also give constructions of locally testable codes (LTCs) with similar parameters. Previous
Optimal Hardness Results for Maximizing . . .
"... We consider the problem of finding a monomial (or a term) that maximizes the agreement rate with a given set of examples over the Boolean hypercube. The problem is motivated by learning of monomials in the agnostic framework of Haussler [12] and Kearns et al. [17]. Finding a monomial with the highes ..."
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this result to ɛ = 2 − log1−λ n for any constant λ> 0 under the assumption that NP � ⊆ RTIME(npoly log(n)), thus also obtaining an inapproximability factor of 2log1−λ n for the symmetric problem of minimizing disagreements. This improves on the log n hardness of approximation factor due to Kearns et al
On the minimum number of wavelengths in multicast trees in WDM networks
 Networks
, 2005
"... We consider the problem of minimizing the number of wavelengths needed to connect a given multicast set in a multihop WDM optical network. This problem was introduced and studied by Li et al. (Networks, 35(4), 260–265, 2000) who showed that it is NPcomplete. They also presented an approximation a ..."
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Cited by 2 (0 self)
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onstrating that their claim cannot be correct—the approximation ratio is(n), even though the subgraph induced by every wavelength is connected, where n is the number of nodes in the network. In fact, we show that the problem cannot be approximated within O(2log 1/2m) unless NP DTIME(npoly log n) for any constant > 0
Extractors and Pseudorandom Generators
 Journal of the ACM
, 1999
"... We introduce a new approach to constructing extractors. Extractors are algorithms that transform a "weakly random" distribution into an almost uniform distribution. Explicit constructions of extractors have a variety of important applications, and tend to be very difficult to obtain. ..."
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Cited by 113 (6 self)
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We introduce a new approach to constructing extractors. Extractors are algorithms that transform a "weakly random" distribution into an almost uniform distribution. Explicit constructions of extractors have a variety of important applications, and tend to be very difficult to obtain.
Nearly Linear Time Approximation Schemes for Euclidean TSP and other Geometric Problems
, 1997
"... We present a randomized polynomial time approximation scheme for Euclidean TSP in ! 2 that is substantially more efficient than our earlier scheme in [2] (and the scheme of Mitchell [21]). For any fixed c ? 1 and any set of n nodes in the plane, the new scheme finds a (1+ 1 c )approximation to ..."
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Cited by 93 (3 self)
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to the optimum traveling salesman tour in O(n(log n) O(c) ) time. (Our earlier scheme ran in n O(c) time.) For points in ! d the algorithm runs in O(n(log n) (O( p dc)) d\Gamma1 ) time. This time is polynomial (actually nearly linear) for every fixed c; d. Designing such a polynomialtime algorithm
Sublinear Time Algorithms for Metric Space Problems
"... In this paper we give approximation algorithms for the following problems on metric spaces: Furthest Pair, k median, Minimum Routing Cost Spanning Tree, Multiple Sequence Alignment, Maximum Traveling Salesman Problem, Maximum Spanning Tree and Average Distance. The key property of our algorithms i ..."
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Cited by 91 (2 self)
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In this paper we give approximation algorithms for the following problems on metric spaces: Furthest Pair, k median, Minimum Routing Cost Spanning Tree, Multiple Sequence Alignment, Maximum Traveling Salesman Problem, Maximum Spanning Tree and Average Distance. The key property of our algorithms is that their running time is linear in the number of metric space points. As the full specification o`f an npoint metric space is of size \Theta(n 2 ), the complexity of our algorithms is sublinear with respect to the input size. All previous algorithms (exact or approximate) for the problems we consider have running time\Omega\Gamma n 2 ). We believe that our techniques can be applied to get similar bounds for other problems. 1 Introduction In recent years there has been a dramatic growth of interest in algorithms operating on massive data sets. This poses new challenges for algorithm design, as algorithms quite efficient on small inputs (for example, having quadratic running time) ...
Learning Mixtures of Arbitrary Gaussians
 STOC
, 2001
"... Mixtures of gaussian (or normal) distributions arise in a variety of application areas. Many techniques have been proposed for the task of finding the component gaussians given samples from the mixture, such as the EM algorithm, a localsearch heuristic from Dempster, Laird and Rubin (1977). However ..."
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Cited by 91 (6 self)
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Mixtures of gaussian (or normal) distributions arise in a variety of application areas. Many techniques have been proposed for the task of finding the component gaussians given samples from the mixture, such as the EM algorithm, a localsearch heuristic from Dempster, Laird and Rubin (1977). However, such heuristics are known to require time exponential in the dimension (i.e., number of variables) in some cases, even when the number of components is 2. This paper presents the first algorithm that provably learns the component gaussians in time that is polynomial in the dimension. The gaussians may have arbitrary shape provided they satisfy a "nondegeneracy" condition, which requires their highprobability regions to be not "too close" together.
Results 1  10
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449