Self-adjusting grid networks.

Emerging networked systems become increasingly flexible, reconfigurable, and “self-⁎”. This introduces an opportunity to adjust networked systems in a demand-aware manner, leveraging spatial and temporal locality in the workload for online optimizations. However, it also introduces a tradeoff: while more frequent adjustments can improve performance, they also entail higher reconfiguration costs. This paper studies self-adjusting grid networks in which frequently communicating nodes (e.g., virtual machines) are moved topologically closer in an online and demand-aware manner, striking a balance between the benefits and costs of reconfigurations. The paper presents a general Ω(log⁡n) lower bound for this problem, even in scenarios where the demand graph is constant once learned. To demonstrate the challenge of adapting a network to pair-wise communication requests, we also design an O(log⁡n)-competitive algorithm for 1-dimensional grids.