Online Placement of Virtual Machines with Prior Data

Naori, David; Raz, Danny

doi:10.1109/infocom41043.2020.9155339

Cited by 6 publications

(5 citation statements)

References 15 publications

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“…Kesselheim et al. (2014) and Naori and Raz (2019) provided an algorithm with the best‐known CR of

\frac{1}{6.99}

. Our work shares a similar model setting to the online GAP and contributes to the literature by considering the i.i.d.…”

Section: Literature Reviewmentioning

confidence: 91%

“…The first is a greedy algorithm—a widely used benchmark in the literature (Dickerson et al., 2018; Lowalekar et al., 2020; Xu et al., 2019). The second benchmark is based on Algorithm 1 in Naori and Raz (2019), in which the authors studied an online GAP. The problem setting is similar to ours but they assume a random‐order arrival model.…”

Section: Methodsmentioning

confidence: 99%

“…The mixing method improves the CR for the GAP from the best‐known

\frac{1}{8.1}

\frac{1}{6.99}

. The detailed algorithm MIX based on Algorithm 1 in Naori and Raz (2019) is shown in Algorithm 4 in Appendix D.1. The third benchmark, denoted by Fluid Bayes Selector (FBS), is based on Algorithm 4 in Vera and Banerjee (2021), in which they studied a general online allocation problem that shares a similar mathematical formula to ours.…”

Section: Methodsmentioning

confidence: 99%

“…In summary, we test the following algorithms in this section. SAMP1: Samp (α) algorithm (Algorithm 1) with

\alpha =1

. Greedy (GRD): Assign an arriving request v to the resource u with the largest weight on the edge

(u,v)

among all the available resources; if no available resource found, reject v . MIX: An algorithm derived from Naori and Raz (2019). For details refer to Algorithm 4 in Appendix D.1. FBS: Algorithm 4 described in Vera and Banerjee (2021).…”

Section: Methodsmentioning

confidence: 99%

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A nonasymptotic analysis for re‐solving heuristic in online matching

Wang

Yan

Bei

2022

Production and Operations Management

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We investigate an online edge‐weighted bipartite matching problem with general capacity constraints. In this problem, the resources are offline and nonreplenishable with different capacities. Demands arrive online and each requests a certain amount of resources. The goal is to maximize the reward generated by successful matches. We model the offline optimization problem as a deterministic linear program (LP) and present multiple randomized online algorithms based on the solution to the offline LP. We analyze the performance guarantee of each algorithm in terms of its competitive ratio (CR). Importantly, we introduce a re‐solving heuristic that periodically recomputes the offline LP and uses the updated offline solution to guide the online algorithm decisions. We find that the algorithm's CR can be significantly improved when re‐solving at carefully selected time steps. Finally, we investigate the value of the demand distribution in further improving the algorithm efficiency. We conduct extensive numerical studies to demonstrate the efficiency of the proposed algorithms. The effect of market conditions on the algorithm performance is also investigated.

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“…Kesselheim et al. (2014) and Naori and Raz (2019) provided an algorithm with the best‐known CR of

\frac{1}{6.99}

. Our work shares a similar model setting to the online GAP and contributes to the literature by considering the i.i.d.…”

Section: Literature Reviewmentioning

confidence: 91%

Section: Methodsmentioning

confidence: 99%

“…The mixing method improves the CR for the GAP from the best‐known

\frac{1}{8.1}

\frac{1}{6.99}

Section: Methodsmentioning

confidence: 99%

“…In summary, we test the following algorithms in this section. SAMP1: Samp (α) algorithm (Algorithm 1) with

\alpha =1

. Greedy (GRD): Assign an arriving request v to the resource u with the largest weight on the edge

(u,v)

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

A nonasymptotic analysis for re‐solving heuristic in online matching

Wang

Yan

Bei

2022

Production and Operations Management

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show abstract

“…Bipartite matching problems are a fundamental building block in the study of online algorithms with myriad applications from Internet advertising through virtual machine placement in cloud computing to kidney exchange programs [23,24]. These problems have been studied extensively over the last three decades in various online models with aiming at capturing realistic conditions and developing practical algorithms with preferred performance.…”

Section: Introductionmentioning

confidence: 99%

Online Weighted Matching with a Sample

Kaplan¹,

Naori²,

Raz³

2021

Preprint

Self Cite

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We study the classical online bipartite matching problem: One side of the graph is known and vertices of the other side arrive online. It is well known that when the graph is edge-weighted, and vertices arrive in an adversarial order, no online algorithm has a nontrivial competitiveratio. To bypass this hurdle we modify the rules such that the adversary still picks the graph but has to reveal a random part (say half) of it to the player. The remaining part is given to the player in an adversarial order. This models practical scenarios in which the online algorithm has some history to learn from.This way of modeling a history was formalized recently by the authors (SODA 20) and was called the AOS model (for Adversarial Online with a Sample). It allows developing online algorithms for the secretary problem that compete even when the secretaries arrive in an adversarial order. Here we use the same model to attack the much more challenging matching problem.We analyze a natural algorithmic framework that decides how to match an arriving vertex v by applying an offline matching algorithm to v and the sample. We get roughly 1/4 of the maximum weight by applying the offline greedy matching algorithm to the sample and v. Our analysis ties the performance of this algorithm to the performance of the offline greedy matching on the online part and we also prove that it is tight. Surprisingly, when replacing greedy with an optimal algorithm for maximum matching, no constant competitive-ratio can be guaranteed when the size of the sample is comparable to the size of the online part. However, when the sample is quadratic in the size of the online part, we do get a competitive-ratio of 1/e.

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Optimal machine placement based on improved genetic algorithm in cloud computing

Zhao

Zhu

et al. 2021

J Supercomput

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Online Placement of Virtual Machines with Prior Data

Cited by 6 publications

References 15 publications

A nonasymptotic analysis for re‐solving heuristic in online matching

A nonasymptotic analysis for re‐solving heuristic in online matching

Online Weighted Matching with a Sample

Optimal machine placement based on improved genetic algorithm in cloud computing

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