On-line maximum-order induced hereditary subgraph problems

We first study the competitive ratio for the on-line version of the problem of finding a maximum-order induced subgraph satisfying some hereditary property, under the hypothesis that the input graph is revealed by clusters. Next, we focus ourselves on two of the most known instantiations of this problem: the maximum independent set and the maximum clique. Finally, we study a variant of the on-line maximum-weight induced hereditary subgraph problem. Our results can also be seen as general reductions, either from off-line problems to the corresponding on-line versions, or between on-line problems. The concept of reduction was absent, until now, from the on-line computation.