Online Matching for Scheduling Problems

In this work an alternative online variant of the matching problem in bipartite graphs is presented. It is motivated by a scheduling problem in an online environment. In such an environment, a task is unknown up to its disclosure. However, in that moment it is not necessary to take a decision on the service of that particular task. In reality, an online scheduler has to decide on how to use the current resources. Therefore, our problem is called online request server matching (ORSM). It diiers substantially from the online bipartite matching problem of Karp et al. KVV90]. Hence, the analysis of an optimal, deterministic online algorithm for the ORSM problem results in a smaller competitive ratio of 1:5. We also introduce an extension to a weighted bipartite matching problem. A lower bound of p 5+1 2 1:618 and an upper bound of 2 is given for the competitive ratio.