Online Balanced Repartitioning of Dynamic Communication Patterns in Polynomial Time

This paper revisits the online balanced repartitioning problem (introduced by Avin et al. at DISC 2016) which asks for a scheduler that dynamically collocates frequently communicating nodes, in order to reduce communication costs while minimizing migrations in distributed systems. More specifically, communication requests arrive online and need to be served, either remotely across different servers at cost 1, or locally within a server at cost 0; before serving a request, the online scheduler can change the mapping of nodes to servers, i.e., migrate nodes, at cost α per node move. Avin et al. presented a deterministic O (k logk)-competitive algorithm, which is optimal up to a logarithmic factor; however, their algorithm has the drawback that it relies on expensive repartitioning operations which result in a super-polynomial runtime. Our main contribution is a different deterministic algorithm pCrep which achieves the same competitive ratio, but runs in polynomial time. Our algorithm monitors the connectivity of communication requests over time, rather than the density as in prior work; this enables the polynomial runtime.We analyze pCrep both analytically and empirically.