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Distributing Unit Size Workload Packages in Heterogeneous Networks
, 2004
"... The task of balancing dynamically generated work load occurs in a wide range of parallel and distributed applications. Diffusion based schemes, which belong to the class of nearest neighbor load balancing algorithms, are a popular way to address this problem. Originally created to equalize the amoun ..."
Abstract

Cited by 11 (0 self)
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The task of balancing dynamically generated work load occurs in a wide range of parallel and distributed applications. Diffusion based schemes, which belong to the class of nearest neighbor load balancing algorithms, are a popular way to address this problem. Originally created to equalize the amount of arbitrarily divisible load among the nodes of a static and homogeneous network, they have been generalized to heterogeneous topologies. Additionally, some simple diffusion algorithms have been adapted to work in dynamic networks as well. However, if the load is not divisible arbitrarily but consists of indivisible unit size tokens, diffusion schemes are not able to balance the load properly. In this paper we consider the problem of balancing indivisible unit size tokens on heterogeneous systems. By modifying a randomized strategy invented for homogeneous systems, we can achieve an asymptotically minimal expected overload in l1, l2 and l ∞ norm while only slightly increasing the runtime by a logarithmic factor. Our experiments show that this additional factor is usually not required in applications.
Quasirandom Load Balancing
"... 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 random algorithm by keeping the accumulated rounding errors as small as possible. Our new algorithm approximates the idealized p ..."
Abstract

Cited by 11 (7 self)
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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 random algorithm by keeping the accumulated rounding errors as small as possible. Our new algorithm approximates the idealized process (where the tokens are divisible) on important network topologies surprisingly closely. On ddimensional torus graphs with n nodes it deviates from the idealized process only by an additive constant. In contrast to that, the randomized rounding approach of Friedrich and Sauerwald [8] can deviate up to Ω(polylogn) and the deterministic algorithm of Rabani, Sinclair and Wanka [23] 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 also on the hypercubeour algorithm has a smaller deviation from the idealized process than the previous algorithms. To prove these results, we derive several combinatorial andprobabilistic results thatwe believe to beof independent interest. In particular, we show that firstpassage probabilities of a random walk on a path with arbitrary weights can be expressed as a convolution of independent geometric probability distributions. 1
Load balancing of indivisible unit size tokens in dynamic and heterogeneous networks
 PROC. OF ESA’04
, 2004
"... The task of balancing dynamically generated work load occurs in a wide range of parallel and distributed applications. Diffusion based schemes, which belong to the class of nearest neighbor load balancing algorithms, are a popular way to address this problem. Originally created to equalize the amoun ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
The task of balancing dynamically generated work load occurs in a wide range of parallel and distributed applications. Diffusion based schemes, which belong to the class of nearest neighbor load balancing algorithms, are a popular way to address this problem. Originally created to equalize the amount of arbitrarily divisible load among the nodes of a static and homogeneous network, they have been generalized to heterogeneous topologies. Additionally, some simple diffusion algorithms have been adapted to work in dynamic networks as well. However, if the load is not divisible arbitrarily but consists of indivisible unit size tokens, diffusion schemes are not able to balance the load properly. In this paper we consider the problem of balancing indivisible unit size tokens on dynamic and heterogeneous systems. By modifying a randomized strategy invented for homogeneous systems, we can achieve an asymptotically minimal expected overload in l1, l2 and l1 norm while only slightly increasing the runtime by a logarithmic factor. Our experiments show that this additional factor is usually not required in applications.