Computer-Aided Complexity Classification of Dial-a-Ride Problems

Paepe, Willem E. de; Lenstra, Jan Karel; Sgall, Jiřį́; Sitters, René; Stougie, Leen

doi:10.1287/ijoc.1030.0052

Cited by 48 publications

(33 citation statements)

References 24 publications

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“…E-mail address: sbock@winfor.de can be found in Tsitsiklis (1992) and partly in De Paepe, Lenstra, Sgall, Sitters, and Stougie (2004). Based on the findings of Afrati, Cosmadakis, Papadimitriou, Papageorgiou, and Papakostantinou (1986), Tsitsiklis additionally resolved the complexity status of some other problem variants.…”

Section: Introduction and Literature Reviewmentioning

confidence: 95%

Solving the traveling repairman problem on a line with general processing times and deadlines

Bock

2015

European Journal of Operational Research

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Section: Introduction and Literature Reviewmentioning

confidence: 95%

Solving the traveling repairman problem on a line with general processing times and deadlines

Bock

2015

European Journal of Operational Research

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“…Without release times, we prove they are NP-hard for capacity c ≥ 2. Our reductions are from the circular arc coloring problem, which is also used in a reduction for minimizing the sum of completion times of Dial-A-Ride on the line with capacity c = 1 [9]. In the classification of closed dial-a-ride problems in [9], offline TSP on the line is the problem 1|s = t, d j |line|C max .…”

Section: The Offline Problemmentioning

confidence: 99%

“…Our reductions are from the circular arc coloring problem, which is also used in a reduction for minimizing the sum of completion times of Dial-A-Ride on the line with capacity c = 1 [9]. In the classification of closed dial-a-ride problems in [9], offline TSP on the line is the problem 1|s = t, d j |line|C max . De Paepe et al [9] claim Tsitsiklis [22] shows a polynomial algorithm, but this is for the open version.…”

Section: The Offline Problemmentioning

confidence: 99%

Tight Bounds for Online TSP on the Line

Bjelde¹,

Disser²,

Hackfeld³

et al. 2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We consider the online traveling salesperson problem (TSP), where requests appear online over time on the real line and need to be visited by a server initially located at the origin. We distinguish between closed and open online TSP, depending on whether the server eventually needs to return to the origin or not. While online TSP on the line is a very natural online problem that was introduced more than two decades ago, no tight competitive analysis was known to date. We settle this problem by providing tight bounds on the competitive ratios for both the closed and the open variant of the problem. In particular, for closed online TSP, we provide a 1.64-competitive algorithm, thus matching a known lower bound. For open online TSP, we give a new upper bound as well as a matching lower bound that establish the remarkable competitive ratio of 2.04.Additionally, we consider the online Dial-A-Ride problem on the line, where each request needs to be transported to a specified destination. We provide an improved non-preemptive lower bound of 1.75 for this setting, as well as an improved preemptive algorithm with competitive ratio 2.41.Finally, we generalize known and give new complexity results for the underlying offline problems. In particular, we give an algorithm with running

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“…An overview of different problem vari-J Sched ants of the Line-TRP (among other dial-a-ride problems) and their complexity status can be found in De Paepe et al (2004). More recently, this overview was updated and supplemented with a new complexity result for a specific variant with delivery times and deadlines in Bock (2015).…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Finding optimal tour schedules on transportation paths under extended time window constraints

Bock

2016

J Sched

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This paper addresses time-critical routing on a given path under release dates and deadline restrictions, while the minimization of the total weighted completion time is pursued. Since there may be destinations with flexible picking area resources that enable a delivery of goods before the defined release date at no additional costs, the wellknown Line-Traveling Repairman problem (Line-TRPTW) is extended into the Line-TRPeTW. The Line-TRPeTW has various practical applications, such as, for example, the tour planning of an inland container ship along a river or that of a vehicle along a coastline. Although the feasibility variant of the Line-TRPTW/Line-TRPeTW is known to be strongly N P-hard, a first practically applicable Branch&Bound procedure is generated. By making use of different dominance rules and lower bounds, a comprehensive computational study proves that instances comprising up to 200 requests and locations are solved to optimality in reasonable time. Moreover, the paper analyzes the complexity of the simpler variant with relaxed release dates at all customer locations. This relaxed variant provides tight lower bounds. Furthermore, the complexity analysis shows that the relaxed problem variant is binary N P-hard even if deadlines are ignored, but can be efficiently solved by a specific Dynamic Programming approach that runs in pseudo-polynomial time.

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Computer-Aided Complexity Classification of Dial-a-Ride Problems

Cited by 48 publications

References 24 publications

Solving the traveling repairman problem on a line with general processing times and deadlines

Solving the traveling repairman problem on a line with general processing times and deadlines

Tight Bounds for Online TSP on the Line

Finding optimal tour schedules on transportation paths under extended time window constraints

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