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2Approximation for Metric TSP
"... This is a polynomialtime 3approximation algorithm for the TSP in a metric space (X, d) ..."
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This is a polynomialtime 3approximation algorithm for the TSP in a metric space (X, d)
Approximating the Metric TSP in linear time
 In Proceedings of WG
, 2008
"... Given a metric graph G = (V, E) of n vertices, i.e., a complete graph with an edge cost function c: V × V ↦ → R≥0 satisfying the triangle inequality, the metricity degree c(x,y) ..."
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Given a metric graph G = (V, E) of n vertices, i.e., a complete graph with an edge cost function c: V × V ↦ → R≥0 satisfying the triangle inequality, the metricity degree c(x,y)
The Metric TSP and the Sum of its Marginal Values
 ABSTRACTS OF THE FALL WORKSHOP ON COMP. GEOM
, 2004
"... This paper introduces a new notion related to the traveling salesperson problem (TSP) — the notion of the TSP ratio. The TSP ratio of a TSP instance I is the sum of the marginal values of the nodes of I divided by the length of the optimal TSP tour on I, where the marginal value of a node i ∈ I is t ..."
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greater than 1. We establish a tight upper bound of 2 on the TSP ratio of any metric TSP. For the TSP on six nodes, we determine the maximum ratio of 1.5 in general, 1.2 for the case of metric TSP, and 10/9 for the geometric TSP in the L1 metric. We also compute the TSP ratio experimentally for a large
The Metric TSP and the Sum of its Marginal Values
, 2004
"... This paper examines the relation between the length of an optimal Traveling Salesman tour and the sum of its nodes ’ marginal values (a node’s marginal value is the difference between the length of an optimal TSP tour over a given node set and the length of an optimal TSP tour over the node set minu ..."
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minus the node). To our knowledge, this problem has not been studied previously. We find that in metric spaces L1, L 4/3, L2, L4, L∞, the event in which the sum of TSP marginal values is greater than the length of the optimal tour is very rare. We present a number of cases for which the sum of marginal
Structural Properties of Hard Metric TSP Inputs∗
"... The metric traveling salesman problem is one of the most prominent APXcomplete optimization problems. An important particularity of this problem is that there is a large gap between the known upper bound and lower bound on the approximability (assuming P 6 = NP). In fact, despite more than 30 year ..."
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The metric traveling salesman problem is one of the most prominent APXcomplete optimization problems. An important particularity of this problem is that there is a large gap between the known upper bound and lower bound on the approximability (assuming P 6 = NP). In fact, despite more than 30
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 ..."
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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
Minimumweight doubletree shortcutting for Metric TSP: Bounding the approximation ratio ✩
, 711
"... 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 problem of findi ..."
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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 problem
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
Structural Properties of Hard Metric TSP Inputs (Extended Abstract)
"... The metric traveling salesman problem is one of the most prominent APXcomplete optimization problems. An important particularity of this problem is that there is a large gap between the known upper bound and lower bound on the approximability (assuming P = NP). In fact, despite more than 30 year ..."
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The metric traveling salesman problem is one of the most prominent APXcomplete optimization problems. An important particularity of this problem is that there is a large gap between the known upper bound and lower bound on the approximability (assuming P = NP). In fact, despite more than 30
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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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
Results 1  10
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10,355