TSP with neighborhoods of varying size

Berg, Mark de; Gudmundsson, Joachim; Katz, Matthew J.; Levcopoulos, Christos; Overmars, Mark H.; Stappen, A. Frank van der

doi:10.1016/j.jalgor.2005.01.010

Cited by 93 publications

(59 citation statements)

References 18 publications

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“…There exists a PTAS for TSPN when the neighborhoods are disjoint unit disks [4]. The most general version of the problem, where regions may overlap and may have varying sizes, is known to be APX-hard [2]. The problem of maximizing the smallest pairwise distance in a set of n points with neighborhoods has also been studied and proved to be NP-hard [6].…”

Section: Related Workmentioning

confidence: 99%

“…Call this the canonical position of the ray. Terminal points from one e-wire are placed at the coordinates (−2, −6) and (2, −6), while terminal points from another e-wire for the clause are placed at positions reflected through the x-axis, i.e., (−2, 6) and (2,6). This way, the terminal points of each pair of e-wires for a clause are positioned symmetrically about a disk in the clause gadget.…”

Section: Clause Gadgetsmentioning

confidence: 99%

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On Minimum-and Maximum-Weight Minimum Spanning Trees with Neighborhoods

Dorrigiv

Fraser

et al. 2013

Approximation and Online Algorithms

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We study optimization problems for the Euclidean minimum spanning tree (MST) on imprecise data. To model imprecision, we accept a set of disjoint disks in the plane as input. From each member of the set, one point must be selected, and the MST is computed over the set of selected points. We consider both minimizing and maximizing the weight of the MST over the input. The minimum weight version of the problem is known as the minimum spanning tree with neighborhoods (MSTN) problem, and the maximum weight version (max-MSTN) has not been studied previously to our knowledge. We provide deterministic and parameterized approximation algorithms for the max-MSTN problem, and a parameterized algorithm for the MSTN problem. Additionally, we present hardness of approximation proofs for both settings.

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Section: Related Workmentioning

confidence: 99%

Section: Clause Gadgetsmentioning

confidence: 99%

On Minimum-and Maximum-Weight Minimum Spanning Trees with Neighborhoods

Dorrigiv

Fraser

et al. 2013

Approximation and Online Algorithms

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“…However, if the regions are allowed to be intersecting connected subsets, the problem remains APX-hard [9,29]. Further restrictions are placed on the regions.…”

Section: Introductionmentioning

confidence: 99%

“…Berg et al [9] gave constant approximation for slightly more general regions of varying size, but are still disjoint, fat and convex. Elbassioni et al [14] generalized this to the discrete case where each neighborhood consists of a discrete set of points in a fat though not necessarily convex region, and gave a constant approximation.…”

Section: Introductionmentioning

confidence: 99%

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A QPTAS for TSP with Fat Weakly Disjoint Neighborhoods in Doubling Metrics

Chan

Elbassioni

2011

Discrete Comput Geom

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We consider the Traveling Salesman Problem with Neighborhoods (TSPN) in doubling metrics. The goal is to find a shortest tour that visits each of a collection of subsets (regions or neighborhoods) in the underlying metric space. We give a QPTAS when the regions are what we call -fat weakly disjoint. This notion combines the existing notions of diameter variation, fatness and disjointness for geometric objects and generalizes these notions to any arbitrary metric space. Intuitively, the regions can be grouped into a bounded number of types, where in each type, the regions have similar upper bounds for their diameters, and each such region can designate a point such that these points are far away from one another.Our result generalizes the PTAS for TSPN on the Euclidean plane by Mitchell [27] and the QPTAS for TSP on doubling metrics by Talwar [30]. We also observe that our techniques directly extend to a QPTAS for the Group Steiner Tree Problem on doubling metrics, with the same assumption on the groups.

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Optimization approaches for civil applications of unmanned aerial vehicles (UAVs) or aerial drones: A survey

et al. 2018

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Unmanned aerial vehicles (UAVs), or aerial drones, are an emerging technology with significant market potential. UAVs may lead to substantial cost savings in, for instance, monitoring of difficult‐to‐access infrastructure, spraying fields and performing surveillance in precision agriculture, as well as in deliveries of packages. In some applications, like disaster management, transport of medical supplies, or environmental monitoring, aerial drones may even help save lives. In this article, we provide a literature survey on optimization approaches to civil applications of UAVs. Our goal is to provide a fast point of entry into the topic for interested researchers and operations planning specialists. We describe the most promising aerial drone applications and outline characteristics of aerial drones relevant to operations planning. In this review of more than 200 articles, we provide insights into widespread and emerging modeling approaches. We conclude by suggesting promising directions for future research.

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TSP with neighborhoods of varying size

Cited by 93 publications

References 18 publications

On Minimum-and Maximum-Weight Minimum Spanning Trees with Neighborhoods

On Minimum-and Maximum-Weight Minimum Spanning Trees with Neighborhoods

A QPTAS for TSP with Fat Weakly Disjoint Neighborhoods in Doubling Metrics

Optimization approaches for civil applications of unmanned aerial vehicles (UAVs) or aerial drones: A survey

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