Balanced Allocation on Graphs: A Random Walk Approach

Pourmiri, Ali

doi:10.1007/978-3-319-42634-1_27

Cited by 5 publications

(6 citation statements)

References 12 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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“…More specifically, the power-of-d choices scaling doesn't hold if the number of bins sampled is some finite number d. Sampling using a single random walk on a graph has also been utilized to probe bins in balls-in-bins models. Pourmiri [12] proposed and analyzed the scheme where the placement bin for ball i is sampled using minimally loaded bins from a specific subset of locations visited by a single non-backtracking random walk of length lr G = o(log(n)) (where l = o(log(n)) and r G ∼ log log(n)) on a high girth d-regular graph between the bins, which starts from a uniformly random position in the graph. It is shown for sparse d-regular graphs (d ∈ [3, O(log(n))]) with high girth that when l ≥ 4 log n/ log k, the maximum load is O(log log n/ log(l/ log n/ log k)) with high probability.…”

Section: Introductionmentioning

confidence: 99%

“…It is shown for sparse d-regular graphs (d ∈ [3, O(log(n))]) with high girth that when l ≥ 4 log n/ log k, the maximum load is O(log log n/ log(l/ log n/ log k)) with high probability. Again a salient feature of [12] is the correlated sampling of bins for each balls, but with independence of the sampling set across balls.…”

Section: Introductionmentioning

confidence: 99%

Balanced Allocation on Graphs with Random Walk Based Sampling

Tang

Subramanian

2018

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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In the standard ball-in-bins experiment, a well-known scheme is to sample d bins independently and uniformly at random and put the ball into the least loaded bin. It can be shown that this scheme yields a maximum load of log log n/ log d + O(1) with high probability.Subsequent work analyzed the model when at each time, d bins are sampled through some correlated or non-uniform way. However, the case when the sampling for different balls are correlated are rarely investigated. In this paper we propose three schemes for the ball-in-bins allocation problem. We assume that there is an underlying k-regular graph connecting the bins. The three schemes are variants of power-of-d choices, except that the sampling of d bins at each time are based on the locations of d independently moving non-backtracking random walkers, with the positions of the random walkers being reset when certain events occurs. We show that under some conditions for the underlying graph that can be summarized as the graph having large enough girth, all three schemes can perform as well as power-of-d, so that the maximum load is bounded by log log n/ log d + O(1) with high probability.high probability, where 1 < φ d < 2 [15]. Kenthapadi and Panigraphy [9] analyzed the scheme where d = 2 bins are sampled through picking a random edge of an underlying graph G, where G is assumed to be almost n ε regular for some 0 < ε < 1. It was shown that this scheme yields a maximum load of log log n + O(1/ε) [9]. As a comparison, Azar's model corresponds to the case that G is a complete graph. Godfrey [6] then generalized the results to the case where an indefinite number of bins are sampled through randomly picking a subset B i ⊂ [n] according to some probability measure. It was shown that, when the size of the subset is approximately Θ(log n), and for each bin j ∈ [n], the probability that j ∈ B i is at the same order of (log n)/n, the maximum load is Θ(1) with high probability. A salient feature of the scheme in [6] is that the subsets of bins can be arbitrarily correlated across balls, and only when Θ(log n) bins get sampled is there sufficient spread in the selections. More specifically, the power-of-d choices scaling doesn't hold if the number of bins sampled is some finite number d. Sampling using a single random walk on a graph has also been utilized to probe bins in balls-in-bins models. Pourmiri [12] proposed and analyzed the scheme where the placement bin for ball i is sampled using minimally loaded bins from a specific subset of locations visited by a single non-backtracking random walk of length lr G = o(log(n)) (where l = o(log(n)) and r G ∼ log log(n)) on a high girth d-regular graph between the bins, which starts from a uniformly random position in the graph. It is shown for sparse d-regular graphs (d ∈ [3, O(log(n))]) with high girth that when l ≥ 4 log n/ log k, the maximum load is O(log log n/ log(l/ log n/ log k)) with high probability. Again a salient feature of [12] is the correlated sampling of bins for each balls, but with independence of th...

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Balanced Allocation on Graphs: A Random Walk Approach

Cited by 5 publications

References 12 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 Graphs with Random Walk Based Sampling

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