Balanced allocation on graphs: A random walk approach

Pourmiri, Ali

doi:10.1002/rsa.20875

Cited by 6 publications

(7 citation statements)

References 15 publications

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“…Communication Cost vs. Load Balancing trade-off has been investigated in [24], [25], [26], [27], [28], [29], and [30], without considering the effect of cache size limitation. Although the works [24], [25], and [26] have mentioned this trade-off, non of them provides a rigorous analysis.…”

Section: Related Workmentioning

confidence: 99%

“…In contrast to the standard balls and bins model, the works [27], [28], [29], and [30] introduced the effect of proximity constraint to the ball and bins framework. In the standard balls and bins model, each ball (request) picks two bins (servers) independently and uniformly at random and it is then allocated to the one with lesser load [6].…”

Section: Related Workmentioning

confidence: 99%

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Storage, Communication, and Load Balancing Trade-off in Distributed Cache Networks

Siavoshani

Pourmiri

Shariatpanahi

2018

IEEE Trans. Parallel Distrib. Syst.

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Abstract-We consider load balancing in a network of caching servers delivering contents to end users. Randomized load balancing via the so-called power of two choices is a wellknown approach in parallel and distributed systems. In this framework, we investigate the tension between storage resources, communication cost, and load balancing performance. To this end, we propose a randomized load balancing scheme which simultaneously considers cache size limitation and proximity in the server redirection process.In contrast to the classical power of two choices setup, since the memory limitation and the proximity constraint cause correlation in the server selection process, we may not benefit from the power of two choices. However, we prove that in certain regimes of problem parameters, our scheme results in the maximum load of order Θ(log log n) (here n is the network size). This is an exponential improvement compared to the scheme which assigns each request to the nearest available replica. Interestingly, the extra communication cost incurred by our proposed scheme, compared to the nearest replica strategy, is small. Furthermore, our extensive simulations show that the trade-off trend does not depend on the network topology and library popularity profile details.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Storage, Communication, and Load Balancing Trade-off in Distributed Cache Networks

Siavoshani

Pourmiri

Shariatpanahi

2018

IEEE Trans. Parallel Distrib. Syst.

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“…From the theoretical viewpoint, in the standard balls and bins model, each ball (request) picks two bins (servers) independently and uniformly at random and it is then allocated to the one with lesser load [5]. However, memory limitation and proximity principle in cache networks makes the bins choices correlated which resembles the balls and bins model with related choices (e.g., see [23], [10], [24], and [25]). Our result also resides in this category, which is specific to cache networks with memory limitation and proximity constraint.…”

Section: Related Workmentioning

confidence: 99%

Proximity-Aware Balanced Allocations in Cache Networks

Pourmiri

Siavoshani

Shariatpanahi

2017

2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS)

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We consider load balancing in a network of caching servers delivering contents to end users. Randomized load balancing via the so-called power of two choices is a wellknown approach in parallel and distributed systems that reduces network imbalance. In this paper, we propose a randomized load balancing scheme which simultaneously considers cache size limitation and proximity in the server redirection process.Since the memory limitation and the proximity constraint cause correlation in the server selection process, we may not benefit from the power of two choices in general. However, we prove that in certain regimes, in terms of memory limitation and proximity constraint, our scheme results in the maximum load of order Θ(log log n) (here n is the number of servers and requests), and at the same time, leads to a low communication cost. This is an exponential improvement in the maximum load compared to the scheme which assigns each request to the nearest available replica. Finally, we investigate our scheme performance by extensive simulations.

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“…Godfrey showed that the maximum load is constant. Balanced allocation on graphs and hypergraphs has been further studied in [3,4,18,19]. In the aforementioned works, either the underlying graph is fixed during the process or, in the hypergraph setting, the number d of choices satisfies d = Ω(log n).…”

Section: Introductionmentioning

confidence: 99%

Balanced Allocation on Hypergraphs

Greenhill¹,

Mans²,

Pourmiri³

2020

Preprint

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The balls-into-bins model randomly allocates n sequential balls into n bins, as follows: each ball selects a set D of d 2 bins, independently and uniformly at random, then the ball is allocated to a least-loaded bin from D (ties broken randomly). The maximum load is the maximum number of balls in any bin. In 1999, Azar et al. showed that, provided ties are broken randomly, after n balls have been placed the maximum load, is log d log n + O(1), with high probability. We consider this popular paradigm in a dynamic environment where the bins are structured as a dynamic hypergraph. A dynamic hypergraph is a sequence of hypergraphs, say H (t) , arriving over discrete times t = 1, 2, . . ., such that the vertex set of H (t) 's is the set of n bins, but (hyper)edges may change over time. In our model, the t-th ball chooses an edge from H (t) uniformly at random, and then chooses a set D of d 2 random bins from the selected edge. The ball is allocated to a least-loaded bin from D, with ties broken randomly. We quantify the dynamicity of the model by introducing the notion of pair visibility, which measures the number of rounds in which a pair of bins appears within a (hyper)edge. We prove that if, for some ε > 0, a dynamic hypergraph has pair visibility at most n 1−ε , and some mild additional conditions hold, then with high probability the process has maximum load O(log d log n). Our proof is based on a variation of the witness tree technique, which is of independent interest. The model can also be seen as an adversarial model where an adversary decides the structure of the possible sets of d bins available to each ball.

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Balanced allocation on graphs: A random walk approach

Cited by 6 publications

References 15 publications

Storage, Communication, and Load Balancing Trade-off in Distributed Cache Networks

Storage, Communication, and Load Balancing Trade-off in Distributed Cache Networks

Proximity-Aware Balanced Allocations in Cache Networks

Balanced Allocation on Hypergraphs

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