Tight Bounds for Online Vector Scheduling

Modern data centers face a key challenge of effectively serving user requests that arrive online. Such requests are inherently multi-dimensional and characterized by demand vectors over multiple resources such as processor cycles, storage space, and network bandwidth. Typically, different resources require different objectives to be optimized, and \(L_r\) norms of loads are among the most popular objectives considered. To address these problems, we consider the online vector scheduling problem in this paper. Introduced by Chekuri and Khanna (SIAM J of Comp. 2006), vector scheduling is a generalization of classical load balancing, where every job has a vector load instead of a scalar load. In this paper, we resolve the online complexity of the vector scheduling problem and its important generalizations.