The competitiveness of on-line assignments
Journal of Algorithms
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
Improved bicriteria existence theorems for scheduling
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Combining fairness with throughout: online routing with multiple objectives
Journal of Computer and System Sciences - Special issue on Internet algorithms
Fairness in Routing and Load Balancing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Fairness measures for resource allocation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On the Existence of Schedules that are Near-Optimal for both Makespan and Total Weighted Completion time
All-norm approximation algorithms
Journal of Algorithms
Graph Theory With Applications
Graph Theory With Applications
Approximate majorization and fair online load balancing
ACM Transactions on Algorithms (TALG)
Pricing for fairness: distributed resource allocation for multiple objectives
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Improved Bounds for Online Routing and Packing Via a Primal-Dual Approach
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Better bounds for online load balancing on unrelated machines
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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We study an online problem that occurs when the capacities of machines are heterogeneous and all jobs are identical. Each job is associated with a subset, called feasible set, of the machines that can be used to process it. The problem involves assigning each job to a single machine in its feasible set, i.e., to find a feasible assignment. The objective is to maximize the throughput, which is the sum of the bandwidths of the jobs; and minimize the total load, which is the sum of the loads of the machines. In the online setting, the jobs arrive one-by-one and an algorithm must make decisions based on the current state without knowledge of future states. By contrast, in the offline setting, all the jobs with their feasible sets are known in advance to an algorithm. Let m denote the total number of machines, α denote the competitive ratio with respect to the throughput and β denote the competitive ratio with respect to the total load. In this paper, our contribution is that we propose an online algorithm that finds a feasible assignment with a throughput-competitive upper bound $\alpha=O(\sqrt{m})$, and a total-load-competitive upper bound $\beta=O(\sqrt{m})$. We also show a lower bound $\alpha\beta=\Omega(\sqrt{m})$ of the problem in the offline setting, which implies a lower bound $\alpha\beta=\Omega(\sqrt{m})$ of the problem in the online setting.