Results 1  10
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46
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
A PTAS for TSP with neighborhoods among fat regions in the plane
 In Proc. ACMSIAM SODA’07
, 2007
"... The Euclidean TSP with neighborhoods (TSPN) problem seeks a shortest tour that visits a given collection of n regions (neighborhoods). We present the first polynomialtime approximation scheme for TSPN for a set of regions given by arbitrary disjoint fat regions in the plane. This improves substan ..."
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Cited by 26 (1 self)
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The Euclidean TSP with neighborhoods (TSPN) problem seeks a shortest tour that visits a given collection of n regions (neighborhoods). We present the first polynomialtime approximation scheme for TSPN for a set of regions given by arbitrary disjoint fat regions in the plane. This im
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
Approximation algorithms for TSP with neighborhoods in the plane
 J. ALGORITHMS
, 2001
"... In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NPhard. In this paper, we present new approximation results for the TSPN, incl ..."
Abstract

Cited by 89 (9 self)
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In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NPhard. In this paper, we present new approximation results for the TSPN
Finding Maximum Length Tours under Euclidean Norms
, 1998
"... Recently, Barvinok, Johnson, Woeginger, and Woodroofe have shown that the Maximum TSP, i. e., the problem of finding a traveling salesman tour of maximum length, can be solved in polynomial time, provided that distances are computed according to a polyhedral norm in IR d , for some fixed d. They s ..."
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studied difficulties of Euclidean distances. In addition, our result implies NPhardness of the Maximum TSP under polyhedral norms if the number k of facets of the unit ball is not fixed, and NPhardness of the Maximum Scatter TSP for geometric instances, where the objective is to find a tour that maximizes
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 ..."
Abstract
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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
Cooperative TSP
 In Proceedings of the 14th Annual European Symposium on Algorithms
, 2006
"... Abstract. In this paper we introduce and study cooperative variants of the Traveling Salesperson Problem. In these problems a salesperson has to make deliveries to customers who are willing to help in the process. Customer cooperativeness may be manifested in several modes: they may assist by approa ..."
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Cited by 1 (0 self)
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the deliveries are made. All the combinations of cooperationmodes and objective functions are considered, both in weighted undirected graphs and in Euclidean space. We show that most of the problems have a constant approximation algorithm, many of the others admit a PTAS, and a few are solvable in polynomial
A robust ptas for maximum weight independent sets in unit disk graphs
 In WG
, 2004
"... Abstract. A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomialtime approximation scheme for the maximum weight independent set problem in unit disk graphs. In contrast to previously known approximation schemes, our approach does not require a geo ..."
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Cited by 16 (0 self)
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Abstract. A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomialtime approximation scheme for the maximum weight independent set problem in unit disk graphs. In contrast to previously known approximation schemes, our approach does not require a
Pricing on Paths: A PTAS for the Highway Problem
"... In the highway problem, we are given an nedge line graph (the highway), and a set of paths (the drivers), each one with its own budget. For a given assignment of edge weights (the tolls), the highway owner collects from each driver the weight of the associated path, when it does not exceed the budg ..."
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Cited by 12 (3 self)
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. In this paper we present a PTAS for the highway problem, hence closing the complexity status of the problem. Our result is based on a novel randomized dissection approach, which has some points in common with Arora’s quadtree dissection for Euclidean network design [Arora’98]. The basic idea is enclosing
Approximation Results for Kinetic Variants of TSP
 IN PROC. INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES, AND PROGRAMMING
, 1999
"... We study the approximation complexity of certain kinetic variants of the Traveling Salesman Problem in the plane where we consider instances in which each point moves with a fixed constant speed in a fixed direction. We prove the following results. 1. If the points all move with the same velocity, ..."
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Cited by 8 (0 self)
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, then there is a PTAS for the Kinetic TSP. 2. The Kinetic TSP cannot be approximated better than by a factor of two by a polynomial time algorithm unless P=NP, even if there are only two moving points in the instance. 3. The Kinetic TSP cannot be approximated better than by a factor of 2\Omega (pn) by a polynomial
Results 1  10
of
46