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A simple approach for adapting continuous load balancing processes to discrete settings

机译:一种使连续负载均衡过程适应离散设置的简单方法

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We consider the neighbourhood load balancing problem. Given a network of processors and an arbitrary distribution of tasks over the network, the goal is to balance load by exchanging tasks between neighbours. In the continuous model, tasks can be arbitrarily divided and perfectly balanced state can always be reached. This is not possible in the discrete model where tasks are non-divisible. In this paper we consider the problem in a very general setting, where the tasks can have arbitrary weights and the nodes can have different speeds. Given a continuous load balancing algorithm that balances the load perfectly in rounds, we convert the algorithm into a discrete version. This new algorithm is deterministic and balances the load in rounds so that the difference between the average and the maximum load is at most , where d is the maximum degree of the network and is the maximum weight of any task. For general graphs, these bounds are asymptotically lower compared to the previous results. The proposed conversion scheme can be applied to a wide class of continuous processes, including first and second order diffusion, dimension exchange, and random matching processes. For the case of identical tasks, we present a randomized version of our algorithm that balances the load up to a discrepancy of provided that the initial load on every node is large enough.
机译:我们考虑邻域负载平衡问题。给定一个处理器网络并在网络上任意分配任务,目标是通过在邻居之间交换任务来平衡负载。在连续模型中,可以任意划分任务,并且始终可以达到完美的平衡状态。在任务不可分割的离散模型中,这是不可能的。在本文中,我们在非常笼统的环境中考虑问题,其中任务可以具有任意权重,节点可以具有不同的速度。给定一个连续的负载均衡算法,可以完美地均衡负载,我们将该算法转换为离散版本。此新算法是确定性的,可以轮流平衡负载,因此平均负载和最大负载之间的差异最大为,其中d是网络的最大程度,并且是任何任务的最大权重。对于一般图形,与以前的结果相比,这些界限渐近降低。所提出的转换方案可以应用于各种各样的连续过程,包括一阶和二阶扩散,尺寸交换和随机匹配过程。对于相同任务的情况,我们提出了一种算法的随机版本,只要每个节点上的初始负载足够大,就可以平衡负载至差异。

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