Balancing indivisible real-valued loads in arbitrary networks

In parallel computing, a problem is divided into a set of smaller tasks that are distributed across multiple processing elements. Balancing the load of the processing elements is key to achieving good performance and scalability. If the computational costs of the individual tasks vary over time in an unpredictable way, dynamic load balancing aims at migrating them between processing elements so as to maintain load balance. During dynamic load balancing, the tasks amount to indivisible work packets with a real-valued cost. For this case of indivisible, real- valued loads, we analyze the balancing circuit model, a local dynamic load-balancing scheme that does not require global communication. We extend previous analyses to the present case and provide a probabilistic bound for the achievable load balance. Based on an analogy with the offline balls-into-bins problem, we further propose a novel algorithm for dynamic balancing of indivisible, real-valued loads. We benchmark the proposed algorithm in numerical experiments and compare it with the classical greedy algorithm, both in terms of solution quality and communication cost. We find that the increased communication cost of the proposed algorithm is compensated by a higher solution quality, leading on average to about an order of magnitude gain in overall performance.Comment: 22 pages, 5 figure