Approximate Dynamic Balanced Graph Partitioning

Harald Räcke, Stefan Schmid, Ruslan Zabrodin

Abstract: Networked systems are increasingly flexible and reconfigurable. This enables demand-aware infrastructures whose resources can be adjusted according to the traffic pattern they currently serve. This paper revisits the dynamic balanced graph partitioning problem, a generalization of the classic balanced graph partitioning problem. We are given a set P of n = kℓ processes which communicate over time according to a given request sequence σ. The processes are assigned to ℓ servers (each of capacity k), and a scheduler can change this assignment dynamically to reduce communication costs, at cost α per node move. Avin et al. showed an Ω(k) lower bound on the competitive ratio of any deterministic online algorithm, even in a model with resource augmentation, and presented an O(k log k)-competitive online algorithm. We study the offline version of this problem where σ is known to the algorithm. Our main contribution is a polynomial-time algorithm which provides an O(log n)-approximation with resource augmentation. Our algorithm relies on an integer linear program formulation in a metric space with spreading constraints. We relax the formulation to a linear program and employ Bartal's clustering algorithm in a novel way to round it.