Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
The competitiveness of on-line assignments
Journal of Algorithms
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
On-line load balancing of temporary tasks
Journal of Algorithms
Better bounds for online scheduling
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
An improved lower bound for load balancing of tasks with unknown duration
Information Processing Letters
On-Line Load Balancing in a Hierarchical Server Topology
SIAM Journal on Computing
On-Line Load Balancing of Temporary Tasks on Identical Machines
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
On-line algorithms for the channel assignment problem in cellular networks
Discrete Applied Mathematics
An equivalent version of the Caccetta-Häggkvist conjecture in an online load balancing problem
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
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We provide a new approach to the on-line load balancing problem in the case of restricted assignment of temporary weighted tasks. The approach is very general and allows us to derive on-line algorithms whose competitive ratio is characterized by some combinatorial properties of the underlying graph G representing the problem: in particular, the approach consists in applying the greedy algorithm to a suitably constructed subgraph of G. In the paper, we prove the NP-hardness of the problem of computing an optimal or even a c-approximate subgraph, for some constant c1. Nevertheless, we show that, for several interesting problems, we can easily compute a subgraph yielding an optimal on-line algorithm. As an example, the effectiveness of this approach is shown by the hierarchical server model introduced by Bar-Noy et al. (2001). In this case, our method yields simpler algorithms whose competitive ratio is at least as good as the existing ones. Moreover, the algorithm analysis turns out to be simpler. Finally, we give a sufficient condition for obtaining, in the general case, O(n)-competitive algorithms with our technique: this condition holds in the case of several problems for which a @W(n) lower bound is known.