On-line load balancing made simple: Greedy strikes back

AbstractWe 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 c>1. 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 Ω(n) lower bound is known

On-line algorithms for the channel assignment problem in cellular networks

We consider the on-line channel assignment problem in the case of cellular networks and we formalize this problem as an on-line load balancing problem for temporary tasks with restricted assignment. For the latter problem, we provide a general solution (denoted as the cluster algorithm) and we characterize its competitive ratio in terms of the combinatorial properties of the graph representing the network. We then compare the cluster algorithm with the greedy one when applied to the channel assignment problem: it turns out that the competitive ratio of the cluster algorithm is strictly better than the competitive ratio of the greedy algorithm. The cluster method is general enough to be applied to other on-line load balancing problems and, for some topologies, it can be proved to be optimal. (C) 2003 Elsevier B.V. All rights reserved

On-line algorithms for the channel assignment problem in cellular networks

We consider the on-line channel assignment problem in the case of cellular networks and we formalise this problem as an on-line load balancing problem of temporary tasks with restricted assignment. For the latter problem, we provide a general solution (denoted as the cluster algorithm) and we characterise its competitive ratio in terms of the combinatorial properties of the graph representing the network. We then compare the cluster algorithm with the greedy one when applied to the channel assignment problem: It turns out that the competitive ratio of the cluster algorithm is strictly better than the competitive ratio of the greedy algorithm. The cluster method is general enough to be applied to other on-line load balancing problems and, for some topologies, it can be proved to be optimal