News from the Online Traveling Repairman

Krumke, Sven O.; Paepe, Willem E. de; Poensgen, Diana; Stougie, Leen

doi:10.1007/3-540-44683-4_43

Cited by 40 publications

(58 citation statements)

References 11 publications

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“…Krumke, de Paepe, Poensgen, Stougie [24] improved upon this result to give a (1 + √ 2) 2 -competitive deterministic algorithm for the online TRP in general metric spaces as well as a Θ-competitive randomized algorithm, where Θ ≈ 3.64; this result was corrected to Θ ≈ 3.86 in Jaillet and Wagner [20] (see also [25]). The online TRP under advanced information, where cities are revealed to the online algorithm before their release dates, was also considered in [20].…”

Section: Previous Workmentioning

confidence: 94%

Almost sure asymptotic optimality for online routing and machine scheduling problems

Jaillet

Wagner

2009

Networks

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In this paper we study algorithms for online routing and machine scheduling problems.The problems are "online" because the problem instances are revealed incrementally. We first study algorithms for the online Traveling Repairman Problem (TRP), where a single server is to visit a set of locations in a network with the objective of minimizing the sum of weighted completion times. We then analyze well-known online algorithms for a variety of machine scheduling problems, which are appropriate models for many network optimization problems; in the scheduling notation of Graham et al.[18], we consider 1|rj, pmtn| j wjCj, 1|rj| j wjCj, Q|rj, pmtn| j Cj, P |rj| j Cj, Q|rj, pmtn| j wjCj and Q|rj| j wjCj.We introduce general probabilistic assumptions about the problem data as a tool to study the online algorithms for these online combinatorial problems. The algorithms do not utilize the underlying probabilistic assumptions in any way. We prove that these online algorithms are almost surely asymptotically optimal.

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Section: Previous Workmentioning

confidence: 94%

Almost sure asymptotic optimality for online routing and machine scheduling problems

Jaillet

Wagner

2009

Networks

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“…In the recent past, several dynamic vehicle routing problems have been successfully studied in this framework, under the name of the online traveling repairman problem (Irani et al, 2004;Jaillet and Wagner, 2006;Krumke et al, 2003), and many interesting insights have been obtained. However, the online algorithm approach has some disadvantages.…”

Section: Online Algorithmsmentioning

confidence: 99%

UAV Routing and Coordination in Stochastic, Dynamic Environments

Enright¹,

Pavone

Savla

2014

Handbook of Unmanned Aerial Vehicles

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Recent years have witnessed great advancements in the science and technology for unmanned aerial vehicles (UAVs), e.g., in terms of autonomy, sensing, and networking capabilities. This chapter surveys algorithms on task assignment and scheduling for one or multiple UAVs in a dynamic environment, in which targets arrive at random locations at random times, and remain active until one of the UAVs flies to the target's location and performs an on-site task. The objective is to minimize some measure of the targets' activity, e.g., the average amount of time during which a target remains active. The chapter focuses on a technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. The main advantage of this approach is its ability to provide analytical estimates of the performance of the UAV system on a given problem, thus providing insight into how performance is affected by design and environmental parameters, such as the number of UAVs and the target distribution. In addition, the approach provides provable guarantees on the system's performance with respect to an ideal optimum. To illustrate this approach, a variety of scenarios are considered, ranging from the simplest case where one UAV moves along continuous paths and has unlimited sensing capabilities, to the case where the motion of the UAV is subject to curvature constraints, and finally to the case where the UAV has a finite sensor footprint. Finally, the problem of cooperative routing algorithms for multiple UAVs is considered, within the same queueing-theoretical framework, and with a focus on control decentralization.

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“…We call the algorithm achieving the bound Group Interval (Algorithm 2), as it can be seen as a multi-server generalization of algorithm Interval [16]. The algorithm is well defined since the time between two departures of the same group is enough for the group to complete its first schedule and return to the origin:…”

Section: The K-traveling Repairman Problem Theorem 32 There Is a Dementioning

confidence: 99%

“…The first paper by Ausiello et al [3] introduced the model for the online traveling salesman problem. Later works investigated competitiveness of the more general dial-a-ride problems [1,11] and studied different objective functions or different adversarial models [2,4,13,16,17,20]. A summary of single server results is contained in the thesis [19].…”

Section: Introductionmentioning

confidence: 99%

Online k-Server Routing Problems

Bonifaci

Stougie

2008

Theory Comput Syst

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Abstract.In an online k-server routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (k-Traveling Salesman Problem) and minimizing the average completion time (k-Traveling Repairman Problem). We give competitive algorithms, resource augmentation results and lower bounds for k-server routing problems on several classes of metric spaces. Surprisingly, in some cases the competitive ratio is dramatically better than that of the corresponding single server problem. Namely, we give a 1 + O((log k)/k)-competitive algorithm for the k-Traveling Salesman Problem and the k-Traveling Repairman Problem when the underlying metric space is the real line. We also prove that similar results cannot hold for the Euclidean plane.

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News from the Online Traveling Repairman

Cited by 40 publications

References 11 publications

Almost sure asymptotic optimality for online routing and machine scheduling problems

Almost sure asymptotic optimality for online routing and machine scheduling problems

UAV Routing and Coordination in Stochastic, Dynamic Environments

Online k-Server Routing Problems

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