Online Makespan Minimization with Parallel Schedules

Albers, Susanne; Hellwig, Matthias

doi:10.1007/s00453-016-0172-5

Cited by 25 publications

(30 citation statements)

References 43 publications

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“…While edge-coloring has not previously been studied in the framework of advice complexity, many other online problems have, see e.g. [1,2,4,[6][7][8][9]11,12,[16][17][18][19][20]22,29,30]. We remark that, contrary to edge-coloring, for several of the problems studied in the literature, sublinear advice (in the number of requests) suffice to achieve a competitive ratio better than that of the best deterministic algorithm without advice.…”

Section: Introductionmentioning

confidence: 86%

Optimal Online Edge Coloring of Planar Graphs with Advice

Mikkelsen

2015

Lecture Notes in Computer Science

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Abstract. Using the framework of advice complexity, we study the amount of knowledge about the future that an online algorithm needs to color the edges of a graph optimally, i.e., using as few colors as possible. For graphs of maximum degree ∆, it follows from Vizing's Theorem that O(m log ∆) bits of advice suffice to achieve optimality, where m is the number of edges. We show that for graphs of bounded degeneracy (a class of graphs including e.g. trees and planar graphs), only O(m) bits of advice are needed to compute an optimal solution online, independently of how large ∆ is. On the other hand, we show that Ω(m) bits of advice are necessary just to achieve a competitive ratio better than that of the best deterministic online algorithm without advice. Furthermore, we consider algorithms which use a fixed number of advice bits per edge (our algorithm for graphs of bounded degeneracy belongs to this class of algorithms). We show that for bipartite graphs, any such algorithm must use at least Ω(m log ∆) bits of advice to achieve optimality.

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Section: Introductionmentioning

confidence: 86%

Optimal Online Edge Coloring of Planar Graphs with Advice

Mikkelsen

2015

Lecture Notes in Computer Science

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“…For the deterministic preemptive setting, Chen et al [11] provide a tight bound of e e−1 for large values of m. More recently, various extension of this basic case have emerged. In resource augmentation settings the algorithm receives some extra resources like machines with higher speed [29], parallel schedules [5,32], or a reordering buffer [14,32]. In a related setting, the algorithm might be allowed to migrate jobs [37].…”

Section: Related Workmentioning

confidence: 99%

Scheduling with Testing on Multiple Identical Parallel Machines

Albers,

Eckl

2021

Preprint

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Scheduling with testing is a recent online problem within the framework of explorable uncertainty motivated by environments where some preliminary action can influence the duration of a task. Jobs have an unknown processing time that can be explored by running a test. Alternatively, jobs can be executed for the duration of a given upper limit. We consider this problem within the setting of multiple identical parallel machines and present competitive deterministic algorithms and lower bounds for the objective of minimizing the makespan of the schedule. In the non-preemptive setting, we present the SBS algorithm whose competitive ratio approaches 3.1016 if the number of machines becomes large. We compare this result with a simple greedy strategy and a lower bound which approaches 2. In the case of uniform testing times, we can improve the SBS algorithm to be 3-competitive. For the preemptive case we provide a 2-competitive algorithm and a tight lower bound which approaches the same value.

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“…A practical application of this algorithm was shown by Kamali and Ortiz [14], who applied it in the Burrows-Wheeler transform compression. More work on parallel online algorithms include parallel scheduling [1], finding independent sets [10] and the "multiple-cow" version of the linear search problem [17].…”

Section: Related Work On Parallel Online Algorithmsmentioning

confidence: 99%

Parallel Online Algorithms for the Bin Packing Problem

Fekete

Grosse-Holz

Keldenich

et al. 2020

Approximation and Online Algorithms

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We study parallel online algorithms: For some fixed integer k, a collective of k parallel processes that perform online decisions on the same sequence of events forms a k-copy algorithm. For any given time and input sequence, the overall performance is determined by the best of the k individual total results. Problems of this type have been considered for online makespan minimization; they are also related to optimization with advice on future events, i.e., a number of bits available in advance.We develop Predictive Harmonic 3 (PH3), a relatively simple family of k-copy algorithms for the online Bin Packing Problem, whose joint competitive factor converges to 1.5 for increasing k. In particular, we show that k = 6 suffices to guarantee a factor of 1.5714 for PH3, which is better than 1.57829, the performance of the best known 1-copy algorithm Advanced Harmonic, while k = 11 suffices to achieve a factor of 1.5406, beating the known lower bound of 1.54278 for a single online algorithm. In the context of online optimization with advice, our approach implies that 4 bits suffice to achieve a factor better than this bound of 1.54278, which is considerably less than the previous bound of 15 bits.

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Online Makespan Minimization with Parallel Schedules

Cited by 25 publications

References 43 publications

Optimal Online Edge Coloring of Planar Graphs with Advice

Optimal Online Edge Coloring of Planar Graphs with Advice

Scheduling with Testing on Multiple Identical Parallel Machines

Parallel Online Algorithms for the Bin Packing Problem

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