Self-stabilizing repeated balls-into-bins

Becchetti, Luca; Clementi, Andrea E. F.; Natale, Emanuele; Pasquale, Francesco; Posta, Gustavo

doi:10.1007/s00446-017-0320-4

Cited by 16 publications

(40 citation statements)

References 45 publications

(62 reference statements)

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“…Moreover, if the process starts in a configuration with maximum load O(log n), then the maximum load stays in O(log n) for poly(n) rounds. An interesting connection to our work is that the analysis of [5] is based on an auxiliary Tetris-process. This process can be seen a special version of our 1-Choice process and is defined as follows: starting from a state with at least n/4 empty bins, in each round every non-empty bin deletes one ball.…”

Section: Related Workmentioning

confidence: 91%

“…From an arbitrary initial assignment, the system is shown to recover to the maximum load from [4] within O n 2 ln n rounds in the former and O(n ln n) rounds in the latter case. Becchetti et al [5] consider a similar (but parallel) process. In each round one ball is chosen from every non-empty bin and reallocated to a randomly chosen bin (one Choice per ball).…”

Section: Related Workmentioning

confidence: 99%

“…, where W −1 denotes the lower branch of the Lambert W function 5 . This implies that ∆ ≤ −f •W −1 (− 1 f •n ), since otherwise we would have Ψ(X(t)) < 0, which is clearly a contradiction.…”

Section: Proving Equation (15)mentioning

confidence: 99%

“…A more elaborate scheme (2-Choice) chooses two servers, queries their current loads, and sends the request to a least loaded of them. Both approaches are typically modeled as balls-into-bins processes [2,4,5,7,13,20,22], where requests are represented as balls and servers as bins. While the latter approach leads to considerably better load distributions [4,7], it loses some of its power in synchronous settings, where requests arrive in parallel and cannot take each other into account [2,22].…”

Section: Introductionmentioning

confidence: 99%

“…in each round there is a bin that receives Θ(log n/ log log n) balls. Most other infinite balls-intobins-type processes limit the total number of concurrent balls in the system by n [4,5] and show a fast recovery. Since we do not limit the number of balls, our process can, in principle, result in an arbitrary high system load.…”

Section: Introductionmentioning

confidence: 99%

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Self-Stabilizing Balls and Bins in Batches

et al. 2018

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A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modeled as static balls into bins processes, where m balls (tasks) are to be distributed among n bins (servers). In a seminal work, Azar et al. [4] proposed the sequential strategy Greedy[d] for n = m. Each ball queries the load of d random bins and is allocated to a least loaded of them. Azar et al. showed that d = 2 yields an exponential improvement compared to d = 1. Berenbrink et al. [7] extended this to m n, showing that for d = 2 the maximal load difference is independent of m (in contrast to the d = 1 case). We propose a new variant of an infinite balls-into-bins process. In each round an expected number of λn new balls arrive and are distributed (in parallel) to the bins. Subsequently, each non-empty bin deletes one of its balls. This setting models a set of servers processing incoming requests, where clients can query a server's current load but receive no information * A preliminary version of this paper was published in the proceedings of PODC'16 † The author did some of the research while affiliated with Simon Fraser University. 1 about parallel requests. We study the Greedy[d] distribution scheme in this setting and show a strong self-stabilizing property: for any arrival rate λ = λ(n) < 1, the system load is time-invariant. Moreover, for any (even super-exponential) round t, the maximum system load is (w.h.p.) O 1 1−λ • log n 1−λ for d = 1 and O log n 1−λ for d = 2. In particular, Greedy[2] has an exponentially smaller system load for high arrival rates.

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Section: Related Workmentioning

confidence: 91%

Section: Related Workmentioning

confidence: 99%

Section: Proving Equation (15)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Self-Stabilizing Balls and Bins in Batches

et al. 2018

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Minimizing message size in stochastic communication patterns: fast self-stabilizing protocols with 3 bits

2018

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This paper considers the basic P U LL model of communication, in which in each round, each agent extracts information from few randomly chosen agents. We seek to identify the smallest amount of information revealed in each interaction (message size) that nevertheless allows for efficient and robust computations of fundamental information dissemination tasks. We focus on the Majority Bit Dissemination problem that considers a population of n agents, with a designated subset of source agents. Each source agent holds an input bit and each agent holds an output bit. The goal is to let all agents converge their output bits on the most frequent input bit of the sources (the majority bit). Note that the particular case of a single source agent corresponds to the classical problem of Broadcast (also termed Rumor Spreading). We concentrate on the severe fault-tolerant context of self-stabilization, in which a correct configuration must be reached eventually, despite all agents starting the execution with arbitrary initial states. In particular, the specification of who is a source and what is its initial input bit may be set by an adversary.We first design a general compiler which can essentially transform any self-stabilizing algorithm with a certain property (called "the bitwise-independence property") that uses -bits messages to one that uses only log -bits messages, while paying only a small penalty in the running time. By applying this compiler recursively we then obtain a self-stabilizing Clock Synchronization protocol, in which agents synchronize their clocks modulo some given integer T , withinÕ(log n log T ) rounds w.h.p., and using messages that contain 3 bits only.We then employ the new Clock Synchronization tool to obtain a self-stabilizing Majority Bit Dissemination protocol which converges inÕ(log n) time, w.h.p., on every initial configuration, provided that the ratio of sources supporting the minority opinion is bounded away from half. Moreover, this protocol also uses only 3 bits per interaction.

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Infinite Balanced Allocation via Finite Capacities

Berenbrink

Friedetzky

Hahn

et al. 2021

2021 IEEE 41st International Conference on Distributed Computing Systems (ICDCS)

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We analyze the following infinite load balancing process, modeled as a classical balls-into-bins game: There are n bins (servers) with a limited capacity (buffer) of size c = c(n) 2 N. Given a fixed arrival rate = (n) 2 (0,1), in every round n new balls (requests) are generated. Together with possible leftovers from previous rounds, these balls compete to be allocated to the bins. To this end, every ball samples a bin independently and uniformly at random and tries to allocate itself to that bin. Each bin accepts as many balls as possible until its buffer is full, preferring balls of higher age. At the end of the round, every bin deletes the ball it allocated first.We study how the buffer size c affects the performance of this process. For this, we analyze both the number of balls competing each round (including the leftovers from previous rounds) as well as the worst-case waiting time of individual balls. We show that (i) the number of competing balls is at any (even exponentially large) time bounded with high probability byand that (ii) the waiting time of a given ball is with high probability at most 4 • ln 1/(1 ) / c • (1 1/e) + loglog n + O c . These results indicate a sweet spot for the choice of c around c = ⇥ p log(1/(1 )) . Compared to a related process with infinite capacity [Berenbrink et al., PODC'16], for constant the waiting time is reduced from O(logn) to O(loglogn). Even for large ⇡ 1 1/n we reduce the waiting time from O(logn) to O( p logn).

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Self-stabilizing repeated balls-into-bins

Cited by 16 publications

References 45 publications

Self-Stabilizing Balls and Bins in Batches

Self-Stabilizing Balls and Bins in Batches

Minimizing message size in stochastic communication patterns: fast self-stabilizing protocols with 3 bits

Infinite Balanced Allocation via Finite Capacities

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