Online Coloring of Intervals with Bandwidth

Motivated by resource allocation problems in communication networks, we consider the problem of online interval coloring in the case where the intervals have weights in (0,1] and the total weight of intersecting intervals with the same color must not exceed 1. We present an online algorithm for this problem that achieves a constant competitive ratio. Our algorithm is a combination of an optimal online algorithm for coloring interval graphs and First-Fit coloring, for which we generalize the analysis of Kierstead to the case of non-unit bandwidth.