Dynamic Load Balancing by Random Matchings

Ghosh, Bhaskar; Muthukrishnan, S.

doi:10.1006/jcss.1996.0075

Cited by 72 publications

(50 citation statements)

References 34 publications

(31 reference statements)

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“…The load balancing protocol presented in [7] builds on the idea of generating a matching in the network topology and balancing load along the edges in the matching. Although the basic idea is similar, our work assumes a random overlay network (that we provide using NEWSCAST) and does not require the communications to take place in a matching in this network.…”

Section: Related Workmentioning

confidence: 99%

Gossip-based aggregation in large dynamic networks

Jelasity

Montresor

Babaoğlu

2005

ACM Trans. Comput. Syst.

586

603

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As computer networks increase in size, become more heterogeneous and span greater geographic distances, applications must be designed to cope with the very large scale, poor reliability, and often, with the extreme dynamism of the underlying network. Aggregation is a key functional building block for such applications: it refers to a set of functions that provide components of a distributed system access to global information including network size, average load, average uptime, location and description of hotspots, etc. Local access to global information is often very useful, if not indispensable for building applications that are robust and adaptive. For example, in an industrial control application, some aggregate value reaching a threshold may trigger the execution of certain actions; a distributed storage system will want to know the total available free space; load balancing protocols may benefit from knowing the target average load so as to minimize the load they transfer. We propose a gossip-based protocol for computing aggregate values over network components in a fully decentralized fashion. The class of aggregate functions we can compute is very broad and includes many useful special cases such as counting, averages, sums, products and extremal values. The protocol is suitable for extremely large and highly dynamic systems due to its proactive structure-all nodes receive the aggregate value continuously, thus being able to track any changes in the system. The protocol is also extremely lightweight making it suitable for many distributed applications including peer-to-peer and grid computing systems. We demonstrate the efficiency and robustness of our gossip-based protocol both theoretically and experimentally under a variety of scenarios including node and communication failures.

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Section: Related Workmentioning

confidence: 99%

Gossip-based aggregation in large dynamic networks

Jelasity

Montresor

Babaoğlu

2005

ACM Trans. Comput. Syst.

586

603

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“…1]). On all graphs with second largest eigenvalue in absolute value λ 2 = λ 2 (P), the idealized process with divisible tokens reduces an initial discrepancy K to ℓ within As λ 2 = 1−Θ(log −1 n) for the hypercube and λ 2 = 1−Θ(n −2/d ) for the d-dimensional torus [15], one immediately obtains the following corollary.…”

Section: 1])mentioning

confidence: 93%

“…Due to this restriction, these algorithms take substantially more time, i.e., they run in time at least linear in the initial discrepancy K. Nonetheless, the best known bounds on the discrepancy are only polynomial in n for the torus and Ω(log 5 n) for the hypercube [16]. In another common model, nodes are only allowed to exchange load with at most one neighbor in each time step, see e.g., [11,15,33]. In fact, the aforementioned randomized rounding approach [11] was analyzed in this model.…”

Section: 1])mentioning

confidence: 99%

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Quasirandom Load Balancing

Friedrich¹,

Gairing²,

Sauerwald

2012

SIAM J. Comput.

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Abstract. We propose a simple distributed algorithm for balancing indivisible tokens on graphs. The algorithm is completely deterministic, though it tries to imitate (and enhance) a randomized algorithm by keeping the accumulated rounding errors as small as possible.Our new algorithm surprisingly closely approximates the idealized process (where the tokens are divisible) on important network topologies. On d-dimensional torus graphs with n nodes it deviates from the idealized process only by an additive constant. In contrast, the randomized rounding approach of Friedrich and Sauerwald [11] can deviate up to Ω(polylog(n)) and the deterministic algorithm of Rabani, Sinclair and Wanka [33] has a deviation of Ω(n 1/d ). This makes our quasirandom algorithm the first known algorithm for this setting which is optimal both in time and achieved smoothness. We further show that on the hypercube as well, our algorithm has a smaller deviation from the idealized process than the previous algorithms.To prove these results, we derive several combinatorial and probabilistic results that we believe to be of independent interest. In particular, we show that first-passage probabilities of a random walk on a path with arbitrary weights can be expressed as a convolution of independent geometric probability distributions.1. Introduction. Load balancing is a requisite for the efficient utilization of computational resources in parallel and distributed systems. The aim is to reallocate the load such that afterward, each node has approximately the same load. Load balancing problems have various applications, e.g., for scheduling [37], routing [5], and numerical computation [38,39].Typically, load balancing algorithms iteratively exchange load along edges of an undirected connected graph. In the natural diffusion paradigm, an arbitrary amount of load can be sent along each edge at each step [31,33]. For the idealized case of divisible load, a popular diffusion algorithm is the first-order-scheme by Subramanian and Scherson [36] whose convergence rate is fairly well captured in terms of the spectral gap [27].However, for many applications the assumption of divisible load may be invalid. Therefore, we consider the discrete case where the load can only be decomposed into indivisible unit-size tokens. A very natural question is how much this integrality assumption decreases the efficiency of load balancing. In fact, finding a precise quantitative relationship between the discrete and the idealized case is an open problem posed by many authors, e.g., [9,11,15,16,28,31,33,36].A simple method for approximating the idealized process was analyzed by Rabani, Sinclair, and Wanka [33]. Their approach (which we will call "RSW algorithm") is to round down the fractional flow of the idealized process. They introduce a very useful parameter of the graph called local divergence and prove that it gives tight upper bounds on the deviation between the idealized process and their discrete process. However, one drawback of the RSW algorithm is that it can ...

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“…One of the early formulations of the quantized consensus problem was in [1] where the issue of quantization to implement consensus algorithms was brought to attention and a solution inspired by distributed load balancing of quantized indivisible tasks was proposed [2][3][4][5]. Since then, several approaches were developed to study the issues of quantization for the consensus problem [6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Fast discrete consensus based on gossip for makespan minimization in networked systems

2015

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In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O(n) in both theoretical and empirical comparisons.

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Dynamic Load Balancing by Random Matchings

Cited by 72 publications

References 34 publications

Gossip-based aggregation in large dynamic networks

Gossip-based aggregation in large dynamic networks

Quasirandom Load Balancing

Fast discrete consensus based on gossip for makespan minimization in networked systems

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