The Mobile Server Problem

Feldkord, Björn; Heide, Friedhelm Meyer auf der

doi:10.1145/3364204

Cited by 4 publications

(12 citation statements)

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“…In [12] it was already shown that no online algorithm for our problem can be competitive even on the real line and with just k = 1 server. As a consequence, we employ the following methods to derive bounds independent of the number of requests for the problem: On the one hand we apply resource augmentation as in [12]: i.e., we allow the online algorithm to use a maximum movement distance of (1 + δ)m s . Other than in the case of k = 1, this is not enough to receive algorithms with a competitive ratio independent of time.…”

Section: Our Results and Outline Of The Papermentioning

confidence: 98%

“…We show that, for k ≥ 2, both methods are needed to yield competitive bounds independent of the length of the instance. For k = 1, it was shown in [12] that a locality of requests can improve the competitiveness, but is not necessary to achieve a constant upper bound.…”

Section: Our Results and Outline Of The Papermentioning

confidence: 99%

“…Besides being a direct extension of the Mobile Server problem [12], our work builds on and is related to results surrounding the k-Server and Page Migration problems. These problems have been examined in many variants and especially for the k-Server problem there are many algorithms for special metrics.…”

Section: Related Workmentioning

confidence: 99%

“…In a previous work [12], a subset of the authors considered the scenario with only one mobile resource. The scenario described above was modeled based on the classical Page Migration problem [8]: A single resource can be moved between two points a and b for costs D • d(a, b), where d (a, b) is the distance between a and b and D ≥ 1 is a constant.…”

Section: Introductionmentioning

confidence: 99%

“…The analysis is conducted in the standard framework of online algorithms and competitive analysis. This problem was extended to the Mobile Server problem in [12], which puts a limit on how much the resource (called server) can move in each time step reflecting the idea that the resource can only be moved locally to avoid congestion and have the service available again shortly after the decision to move it.…”

Section: Introductionmentioning

confidence: 99%

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Managing Multiple Mobile Resources

et al. 2021

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We extend the Mobile Server problem introduced in Feldkord and Meyer auf der Heide (TOPC 6(3), 14:1–14:17 2019) to a model where k identical mobile resources, here named servers, answer requests appearing at points in the Euclidean space. To reduce communication costs, the positions of the servers can be adapted by a limited distance ms per round for each server. The costs are measured similarly to the classical Page Migration problem: i.e., answering a request induces costs proportional to the distance to the nearest server, and moving a server induces costs proportional to the distance multiplied with a weight D. We show that, in our model, no online algorithm can have a constant competitive ratio: i.e., one which is independent of the input length n, even if an augmented moving distance of (1 + δ)ms is allowed for the online algorithm. Therefore we investigate a restriction of the power of the adversary dictating the sequence of requests: We demand locality of requests: i.e., that consecutive requests come from points in the Euclidean space with distance bounded by some constant mc. We show constant lower bounds on the competitiveness in this setting (independent of n, but dependent on k, ms and mc). On the positive side, we present a deterministic online algorithm with bounded competitiveness when an augmented moving distance and locality of requests is assumed. Our algorithm simulates any given algorithm for the classical k-Page Migration problem as guidance for its servers and extends it by a greedy move of one server in every round. The resulting competitive ratio is polynomial in the number of servers k, the ratio between mc and ms, the inverse of the augmentation factor 1/δ and the competitive ratio of the simulated k-Page Migration algorithm. We also show how to directly adapt the Double Coverage algorithm (Chrobak et al. SIAM J. Discrete Math. 4(2), 172–181 11) for the k-Server problem to receive an algorithm with improved competitiveness on the line.

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Section: Our Results and Outline Of The Papermentioning

confidence: 98%

Section: Our Results and Outline Of The Papermentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Managing Multiple Mobile Resources

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Toward Online Mobile Facility Location on General Metrics

Ghodselahi,

Kuhn

2023

Theory Comput Syst

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We introduce an online variant of mobile facility location (MFL) (introduced by Demaine et al. (SODA 258–267 2007)). We call this new problem online mobile facility location (OMFL). In the OMFL problem, initially, we are given a set of k mobile facilities with their starting locations. One by one, requests are added. After each request arrives, one can make some changes to the facility locations before the subsequent request arrives. Each request is always assigned to the nearest facility. The cost of this assignment is the distance from the request to the facility. The objective is to minimize the total cost, which consists of the relocation cost of facilities and the distance cost of requests to their nearest facilities. We provide a lower bound for the OMFL problem that even holds on uniform metrics. A natural approach to solve the OMFL problem for general metric spaces is to utilize hierarchically well-separated trees (HSTs) and directly solve the OMFL problem on HSTs. In this paper, we provide the first step in this direction by solving a generalized variant of the OMFL problem on uniform metrics that we call G-OMFL. We devise a simple deterministic online algorithm and provide a tight analysis for the algorithm. The second step remains an open question. Inspired by the k-server problem, we introduce a new variant of the OMFL problem that focuses solely on minimizing movement cost. We refer to this variant as M-OMFL. Additionally, we provide a lower bound for M-OMFL that is applicable even on uniform metrics.

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