Results 1 - 10 of 46

On the Maximum Scatter TSP

by Esther M. Arkin, Yi-Jen Chiang, Joseph S. B. Mitchell, Steven S. Skiena, Tae-cheon Yang , 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) - Add to MetaCart
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

by Joseph S. B. Mitchell - In Proc. ACM-SIAM SODA’07 , 2007
"... The Euclidean TSP with neighborhoods (TSPN) problem seeks a shortest tour that visits a given collection of n re-gions (neighborhoods). We present the first polynomial-time approximation scheme for TSPN for a set of regions given by arbitrary disjoint fat regions in the plane. This im-proves substan ..."
Abstract - Cited by 26 (1 self) - Add to MetaCart
The Euclidean TSP with neighborhoods (TSPN) problem seeks a shortest tour that visits a given collection of n re-gions (neighborhoods). We present the first polynomial-time 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)

by Esther M. Arkin, Yi-Jen Chiang, Joseph S. B. Mitchell, Steven S. Skiena, Tae-Cheon Yang - PROC. ACM-SIAM 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) - Add to MetaCart
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

by Adrian Dumitrescu , Joseph S. B. Mitchell - 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 NP-hard. In this paper, we present new approximation results for the TSPN, incl ..."
Abstract - Cited by 89 (9 self) - Add to MetaCart
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 NP-hard. In this paper, we present new approximation results for the TSPN

Finding Maximum Length Tours under Euclidean Norms

by Sandor P. Fekete , 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 NP-hardness of the Maximum TSP under polyhedral norms if the number k of facets of the unit ball is not fixed, and NP-hardness 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

by Yi-Jen Chiang - 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

Cooperative TSP

by Amitai Armon, Adi Avidor, Oded Schwartz - 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 ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
the deliveries are made. All the combinations of cooperation-modes 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

by Tim Nieberg, Johann Hurink, Walter Kern - In WG , 2004
"... Abstract. A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomial-time 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 ..."
Abstract - Cited by 16 (0 self) - Add to MetaCart
Abstract. A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomial-time 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

by Fabrizio Grandoni, Thomas Rothvoß
"... In the highway problem, we are given an n-edge 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 ..."
Abstract - Cited by 12 (3 self) - Add to MetaCart
. In this paper we present a PTAS for the highway prob-lem, 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 dis-section for Euclidean network design [Arora-’98]. The basic idea is enclosing

Approximation Results for Kinetic Variants of TSP

by Mikael Hammar, Bengt J. Nilsson - 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, ..."
Abstract - Cited by 8 (0 self) - Add to MetaCart
, 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