On Approximating a Geometric Prize-Collecting Traveling Salesman Problem with Time Windows

Bar-Yehuda, Reuven; Even, Guy; Shahar, Shimon

doi:10.1007/978-3-540-39658-1_8

Cited by 12 publications

(16 citation statements)

References 6 publications

(1 reference statement)

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“…Non−disjoint rectangles (5) u (4) u Deadlines Collection C Collection C We first describe the family C1, . .…”

Section: An O(log N) Approximation For Deadline-tspmentioning

confidence: 99%

“…In the approximation algorithms literature, there has been work on geometric versions of this problem. Several constant factor approximations [5,21,15] have been proposed for the case of points on a line. For general graphs, Chekuri and Kumar [8] give a constant-factor approximation when there are a constant number of different deadlines (or time windows).…”

Section: Introductionmentioning

confidence: 99%

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Approximation algorithms for deadline-TSP and vehicle routing with time-windows

Bansal

Blum

Chawla

et al. 2004

Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing

179

204

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Given a metric space G on n nodes, with a start node r and deadlines D(v) for each vertex v, we consider the Deadline-TSP problem of finding a path starting at r that visits as many nodes as possible by their deadlines. We also consider the more general Vehicle Routing with TimeWindows problem, in which each node v also has a releasetime R(v) and the goal is to visit as many nodes as possible within their "time-windows" [R(v), D(v)]. No good approximations were known previously for these problems on general metric spaces. We give an O(log n) approximation algorithm for Deadline-TSP, and extend this algorithm to an O(log 2 n) approximation for the Time-Window problem. We also give a bicriteria approximation algorithm for both problems: Given an > 0, our algorithm produces a log(1/ ) approximation, while exceeding the deadlines by a factor of 1 + . We use as a subroutine for these results a constantfactor approximation that we develop for a generalization of the orienteering problem in which both the start and the end nodes of the path are fixed. In the process, we give a 3-approximation to the orienteering problem, improving on the previously best known 4-approximation of [6].

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“…Non−disjoint rectangles (5) u (4) u Deadlines Collection C Collection C We first describe the family C1, . .…”

Section: An O(log N) Approximation For Deadline-tspmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximation algorithms for deadline-TSP and vehicle routing with time-windows

Bansal

Blum

Chawla

et al. 2004

Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing

179

204

View full text Add to dashboard Cite

show abstract

“…The connection between our problems and the Traveling Salesman Problem (TSP) [4] and its prize-collecting versions [7,9] is equally abstract. The TSP problem considers a set of cities and distances between them and asks for the shortest possible tour that visits each city exactly ones and returns to the original city.…”

Section: Related Workmentioning

confidence: 99%

Customized tour recommendations in urban areas

Gionis

Lappas

Pelechrinis

et al. 2014

Proceedings of the 7th ACM International Conference on Web Search and Data Mining

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The ever-increasing urbanization coupled with the unprecedented capacity to collect and process large amounts of data have helped to create the vision of intelligent urban environments. One key aspect of such environments is that they allow people to effectively navigate through their city. While GPS technology and route-planning services have undoubtedly helped towards this direction, there is room for improvement in intelligent urban navigation. This vision can be fostered by the proliferation of location-based social networks, such as Foursquare or Path, which record the physical presence of users in different venues through check-ins. This information can then be used to enhance intelligent urban navigation, by generating customized path recommendations for users.In this paper, we focus on the problem of recommending customized tours in urban settings. These tours are generated so that they consider (a) the different types of venues that the user wants to visit, as well as the order in which the user wants to visit them, (b) limitations on the time to be spent or distance to be covered, and (c) the merit of visiting the included venues. We capture these requirements in a generic definition that we refer to as the TourRec problem. We then introduce two instances of the TourRec problem, study their complexity, and propose efficient algorithmic solutions. Our experiments on real data collected from Foursquare demonstrate the efficacy of our algorithms and the practical utility of the reported recommendations.

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“…Then, the answer to I is "Yes." REMARK: Bar-Yehuda et al [5] considered the P-1-VRP of maximizing the total weight of early customers in which each customer is associated with a release time less than its due date by a constant. One can verify that our proof also holds if we assign the release times of customers as follows…”

Section: Weighted Number Of Tardy Customersmentioning

confidence: 99%

“…If d < min{2t h,i + t h,k+1 , 2t h,k + t h,i−1 }, then the first tardy customer in S i,k may be selected from i−1 and k + 1. The vehicle chooses the better visiting order from (4) and (5). It holds that…”

Section: Total Weighted Penalty With a Common Due Datementioning

confidence: 99%

Vehicle routing problems with regular objective functions on a path

Liu

2013

Naval Research Logistics

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We investigate the problem of scheduling a fleet of vehicles to visit the customers located on a path to minimize some regular function of the visiting times of the customers. For the single-vehicle problem, we prove that it is pseudopolynomially solvable for any minsum objective and polynomially solvable for any minmax objective. Also, we establish the NP-hardness of minimizing the weighted number of tardy customers and the total weighted tardiness, and present polynomial algorithms for their special cases with a common due date. For the multivehicle problem involving n customers, we show that an optimal solution can be found by solving O(n 2 ) or O(n) single-vehicle problems.

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On Approximating a Geometric Prize-Collecting Traveling Salesman Problem with Time Windows

Cited by 12 publications

References 6 publications

Approximation algorithms for deadline-TSP and vehicle routing with time-windows

Approximation algorithms for deadline-TSP and vehicle routing with time-windows

Customized tour recommendations in urban areas

Vehicle routing problems with regular objective functions on a path

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