On-Line Load Balancing with Task Buffer

On-line load balancing is one of the most important problems for applications with resource allocation. It aims to assign tasks to suitable machines and balance the load among all of the machines, where the tasks need to be assigned to a machine upon arrival. In practice, tasks are not always required to be assigned to machines immediately. In this paper, we propose a novel on-line load balancing model with task buffer, where the buffer can temporarily store tasks as many as possible. Three algorithms, namely LPTCP1_α, LPTCP2_α, and LPTCP3_β, are proposed based on the Longest Processing Time (LPT) algorithm and a variety of planarization algorithms. The planarization algorithms are proposed for reducing the difference among each element in a set. Experimental results show that our proposed algorithms can effectively solve the on-line load balancing problem and have good performance in large scale experiments

Online makespan scheduling with job migration on uniform machines

In the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we allow the online algorithm to change the assignment of up to k jobs at the end for some limited number k. For m identical machines, Albers and Hellwig (Algorithmica 79(2):598–623, 2017) give tight bounds on the competitive ratio in this model. The precise ratio depends on, and increases with, m. It lies between 4/3 and ≈1.4659. They show that k=O(m) is sufficient to achieve this bound and no k=o(n) can result in a better bound. We study m uniform machines, i.e., machines with different speeds, and show that this setting is strictly harder. For sufficiently large m, there is a δ=Θ(1) such that, for m machines with only two different machine speeds, no online algorithm can achieve a competitive ratio of less than 1.4659+δ with k=o(n). We present a new algorithm for the uniform machine setting. Depending on the speeds of the machines, our scheduling algorithm achieves a competitive ratio that lies between 4/3 and ≈1.7992 with k=O(m). We also show that k=Ω(m) is necessary to achieve a competitive ratio below 2. Our algorithm is based on maintaining a specific imbalance with respect to the completion times of the machines, complemented by a bicriteria approximation algorithm that minimizes the makespan and maximizes the average completion time for certain sets of machines