Dynamic Traveling Repair Problem with an Arbitrary Time Window

Azar, Yossi; Vardi, Adi

doi:10.1007/978-3-319-51741-4_2

Cited by 5 publications

(4 citation statements)

References 18 publications

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“…e 1 2, 4, 9 4, 10, 13 e 2 Figure 3: Edges e 1 and e 2 share label 4. If we consider task T 1 associated with e 1 to have possible scheduling intervals (2,4) and (4,9), and task T 2 associated with e 2 to have possible scheduling intervals (4, 10) and (10,13), then a feasible schedule would execute T 1 during (2, 4) and T 2 during (4, 10). However, this does not correspond to an exploration of the edges e 1 and e 2 , since exiting e 1 with label 4 would disallow entry to e 2 with the same label (due to our definition of journeys)!…”

Section: Withinmentioning

confidence: 99%

“…For the Asymmetric TSP where paths may not exist in both directions or the distances might be different depending on the direction, the O(log n)-approximation of [20] was the best known for almost three decades, improved only recently to O(log n/ log log n) [7]. Online TSP-related problems as well as versions of TSP where each node must be visited within a given time window, have also been recently studied [9,34].…”

Section: Introductionmentioning

confidence: 99%

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The Temporal Explorer Who Returns to the Base

Akrida

Mertzios

Spirakis

2019

Lecture Notes in Computer Science

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In this paper we study the problem of exploring a temporal graph (i.e. a graph that changes over time), in the fundamental case where the underlying static graph is a star. The aim of the exploration problem in a temporal star is to find a temporal walk which starts at the center of the star, visits all leafs, and eventually returns back to the center. We initiate a systematic study of the computational complexity of this problem, depending on the number k of time-labels that every edge is allowed to have; that is, on the number k of time points where every edge can be present in the graph. To do so, we distinguish between the decision version StarExp(k) asking whether a complete exploration of the instance exists, and the maximization version MaxStarExp(k) of the problem, asking for an exploration schedule of the greatest possible number of edges in the star. We present here a collection of results establishing the computational complexity of these two problems. On the one hand, we show that both MaxStarExp(2) and StarExp(3) can be efficiently solved in O(n log n) time on a temporal star with n vertices. On the other hand, we show that, for every k ≥ 6, StarExp(k) is NP-complete and MaxStarExp(k) is APX-hard, and thus it does not admit a PTAS, unless P = NP. The latter result is complemented by a polynomial-time 2-approximation algorithm for MaxStarExp(k), for every k, thus proving that MaxStarExp(k) is APX-complete. Finally, we give a partial characterization of the classes of temporal stars with random labels which are, asymptotically almost surely, yes-instances and no-instances for StarExp(k) respectively.

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Section: Withinmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Temporal Explorer Who Returns to the Base

Akrida

Mertzios

Spirakis

2019

Lecture Notes in Computer Science

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“…Online algorithms where requests can be served within some time-window (or more generally, with delay penalties) have recently been given for matching [EKW16, AAC + 17, ACK17], TSP [AV16], set cover [ACKT20], multi-level aggregation [BBB + 16, BFNT17, AT19], 1-server [AGGP17, AT19], network design [AT20], etc. The work closest to ours is that of [AGGP17] who show O(k log 3 n)competitiveness for k-Server with general delay functions, and leave open the problem of getting polylogarithmic competitiveness.…”

Section: Related Workmentioning

confidence: 99%

A Hitting Set Relaxation for $k$-Server and an Extension to Time-Windows

Gupta¹,

Kumar²,

Panigrahi³

2021

Preprint

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We study the k-server problem with time-windows. In this problem, each request i arrives at some point v i of an n-point metric space at time b i and comes with a deadline e i . One of the k servers must be moved to v i at some time in the interval [b i , e i ] to satisfy this request. We give an online algorithm for this problem with a competitive ratio of poly log(n, ∆), where ∆ is the aspect ratio of the metric space. Prior to our work, the best competitive ratio known for this problem was O(k poly log(n)) given by Azar et al. (STOC 2017).Our algorithm is based on a new covering linear program relaxation for k-server on HSTs. This LP naturally corresponds to the min-cost flow formulation of k-server, and easily extends to the case of time-windows. We give an online algorithm for obtaining a feasible fractional solution for this LP, and a primal dual analysis framework for accounting the cost of the solution. Together, they yield a new k-server algorithm with poly-logarithmic competitive ratio, and extend to the time-windows case as well. Our principal technical contribution lies in thinking of the covering LP as yielding a truncated covering LP at each internal node of the tree, which allows us to keep account of server movements across subtrees. We hope that this LP relaxation and the algorithm/analysis will be a useful tool for addressing k-server and related problems.

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“…With the assumption that the arrival process of the intruders is stochastic, [21], [22], [23] consider the perimeter defense problem as a vehicle routing problem and provide insights into the average case analysis of such problems. An important distinction between the online setup of this work from [24] is that the time taken by the intruders to reach the perimeter is fixed and not the part of the input.…”

Section: Introductionmentioning

confidence: 99%

Perimeter Defense using a Turret with Finite Range and Service Times

Bajaj¹,

Bopardikar²,

Moll³

et al. 2023

Preprint

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We consider a perimeter defense problem in a planar conical environment comprising a single turret that has a finite range and non-zero service time. The turret seeks to defend a concentric perimeter against N ≥ 2 intruders. Upon release, each intruder moves radially towards the perimeter with a fixed speed. To capture an intruder, the turret's angle must be aligned with that of the intruder's angle and must spend a specified service time at that orientation. We address offline and online versions of this optimization problem. Specifically, in the offline version, we establish that in general parameter regimes, this problem is equivalent to solving a Travelling Repairperson Problem with Time Windows (TRP-TW). We then identify specific parameter regimes in which there is a polynomial time algorithm that maximizes the number of intruders captured. In the online version, we present a competitive analysis technique in which we establish a fundamental guarantee on the existence of at best (N − 1)competitive algorithms. We also design two online algorithms that are provably 1 and 2-competitive in specific parameter regimes.

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Dynamic Traveling Repair Problem with an Arbitrary Time Window

Cited by 5 publications

References 18 publications

The Temporal Explorer Who Returns to the Base

The Temporal Explorer Who Returns to the Base

A Hitting Set Relaxation for $k$-Server and an Extension to Time-Windows

Perimeter Defense using a Turret with Finite Range and Service Times

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