Online Job Scheduling with <i>K</i> Servers

Abstract

In this paper, we investigate an online job scheduling problem with n jobs and k servers, where the accessibilities between the jobs and the servers are given as a bipartite graph. The scheduler is tasked with minimizing the regret, defined as the difference between the total flow time of the scheduler over T rounds and that of the best-fixed scheduling in hindsight. We propose an algorithm whose regret bounds are O(n 2 √ T ln(nk)) for general bipartite graphs, O((n 2 /k 1/2 ) √ T ln(nk)) for the complete bipartite graphs, and O((n 2 /k) √ T ln(nk) for the disjoint star graphs, respectively. We also give a lower regret bound of Ω((n 2 /k) √ T ) for the disjoint star graphs, implying that our regret bounds are almost optimal.