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292
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 ..."
Abstract

Cited by 797 (39 self)
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vertex cover, maximum satisfiability, maximum cut, metric TSP, Steiner trees and shortest superstring. We also improve upon the clique hardness results of Feige, Goldwasser, Lovász, Safra and Szegedy [42], and Arora and Safra [6] and shows that there exists a positive ɛ such that approximating
Resilient Overlay Networks
, 2001
"... A Resilient Overlay Network (RON) is an architecture that allows distributed Internet applications to detect and recover from path outages and periods of degraded performance within several seconds, improving over today’s widearea routing protocols that take at least several minutes to recover. A R ..."
Abstract

Cited by 1160 (31 self)
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, optimizing applicationspecific routing metrics. Results from two sets of measurements of a working RON deployed at sites scattered across the Internet demonstrate the benefits of our architecture. For instance, over a 64hour sampling period in March 2001 across a twelvenode RON, there were 32 significant
On the Maximum Scatter TSP
, 1996
"... We study the problem of computing a Hamiltonian tour (cycle) or path on a set of points in order to maximize the minimum edge length in the tour or path. This "maximum scatter" TSP is closely related to the bottleneck TSP, and is motivated by applications in manufacturing (e.g., sequencing ..."
Abstract

Cited by 2 (1 self)
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We study the problem of computing a Hamiltonian tour (cycle) or path on a set of points in order to maximize the minimum edge length in the tour or path. This "maximum scatter" TSP is closely related to the bottleneck TSP, and is motivated by applications in manufacturing (e
On the Maximum Scatter TSP (Extended Abstract)
 PROC. ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1997
"... We study the problem of computing a Hamiltonian tour (cycle) or path on a set of points in order to maximize the minimum edge length in the tour or path. This "maximum scatter" TSP is closely related to the bottleneck TSP, and is motivated by applications in manufacturing (e.g., sequencing ..."
Abstract

Cited by 1 (0 self)
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We study the problem of computing a Hamiltonian tour (cycle) or path on a set of points in order to maximize the minimum edge length in the tour or path. This "maximum scatter" TSP is closely related to the bottleneck TSP, and is motivated by applications in manufacturing (e
DoubleTree Approximations for Metric TSP: Is the Best One Good Enough?
, 2004
"... The Metric Travelling Salesman Problem (TSP) is a classical NPhard optimisation problem. The doubletree heuristic for Metric TSP yields a space of approximate solutions, each of which is within a factor of 2 from the optimum. Such an approach raises two natural questions: can we nd eciently a ..."
Abstract

Cited by 1 (0 self)
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The Metric Travelling Salesman Problem (TSP) is a classical NPhard optimisation problem. The doubletree heuristic for Metric TSP yields a space of approximate solutions, each of which is within a factor of 2 from the optimum. Such an approach raises two natural questions: can we nd eciently
Fast minimumweight doubletree shortcutting for Metric TSP
 In Proceedings of the 6th WEA. Lecture Notes in Computer Science
"... Abstract. The Metric Traveling Salesman Problem (TSP) is a classical NPhard optimization problem. The doubletree shortcutting method for Metric TSP yields an exponentiallysized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the proble ..."
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Cited by 4 (2 self)
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Abstract. The Metric Traveling Salesman Problem (TSP) is a classical NPhard optimization problem. The doubletree shortcutting method for Metric TSP yields an exponentiallysized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider
Deterministic 7/8approximation for the metric maximum TSP
 In Proc. 11th Int. Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX
, 2008
"... We present the first 7/8approximation algorithm for the maximum traveling salesman problem with triangle inequality. Our algorithm is deterministic. This improves over both the randomized algorithm of Hassin and Rubinstein [2] with expected approximation ratio of 7/8−O(n−1/2) and the deterministic ..."
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Cited by 7 (0 self)
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We present the first 7/8approximation algorithm for the maximum traveling salesman problem with triangle inequality. Our algorithm is deterministic. This improves over both the randomized algorithm of Hassin and Rubinstein [2] with expected approximation ratio of 7/8−O(n−1
New Approximation results for the Maximum Scatter TSP
 ALGORITHMICA
, 2004
"... We consider the following maximum scatter traveling salesperson problem (TSP): given an edgeweighted complete graph (S, E), find a Hamiltonian path or cycle such that the length of a shortest edge is maximized. In other words, the goal is to have each point far away (most "scattered") f ..."
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We consider the following maximum scatter traveling salesperson problem (TSP): given an edgeweighted complete graph (S, E), find a Hamiltonian path or cycle such that the length of a shortest edge is maximized. In other words, the goal is to have each point far away (most "scattered
On Hierarchical Routing in Doubling Metrics
"... We study the problem of routing in doubling metrics, and show how to perform hierarchical routing in such metrics with small stretch and compact routing tables (i.e., with small amount of routing information stored at each vertex). We say that a metric (X; d) has doubling dimension dim(X)at most f ..."
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Cited by 67 (7 self)
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for doubling metrics than those obtained from the routing tables above; for o / ? 0, we give algorithms to construct (1 + o /)stretch spanners for a metric (X; d) with maximum degree at most (2 + 1=o /)O(dim(X)), matching the results of Das et al.for Euclidean metrics.
Improved approximation algorithms for metric Max TSP
 In Proc. 13th Annual European Symposium on Algorithms (ESA’05), volume 3669 of LNCS
, 2005
"... We present two polynomialtime approximation algorithms for the metric case of the maximum traveling salesman problem. One of them is for directed graphs and its approximation ratio is 2735. The other is for undirected graphs and its approximation ratio is 78−o(1). Both algorithms improve on the pre ..."
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Cited by 11 (0 self)
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We present two polynomialtime approximation algorithms for the metric case of the maximum traveling salesman problem. One of them is for directed graphs and its approximation ratio is 2735. The other is for undirected graphs and its approximation ratio is 78−o(1). Both algorithms improve
Results 1  10
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292