The performance of many large-scale and data-intensive distributed systems critically depends on the capacity of the interconnecting network. This paper is motivated by the vision of self-adjusting infrastructures whose resources can be adjusted according to the workload they currently serve, in a demand-aware manner. Such dynamic adjustments can be exploited to improve network utilization and hence performance, by dynamically moving frequently interacting communication partners closer, e.g., collocating them in the same server or datacenter rack. In particular, we revisit the online balanced graph partitioning problem which captures the fundamental tradeoff between the benefits and costs of dynamically collocating communication partners. The demand is modelled as a sequence $\sigma$ (revealed in an online manner) of communication requests between $n$ processes, each of which is running on one of the $\ell$ servers. Each server has capacity $k=n/\ell$, hence, the processes have to be scheduled in a balanced manner across the servers. A request incurs cost $1$, if the requested processes are located on different servers, otherwise the cost is 0. A process can be migrated to a different server at cost $1$. This paper presents the first online algorithm for online balanced graph partitioning achieving a polylogarithmic competitive ratio for the fundamental case of ring communication patterns. Specifically, our main contribution is a $O(\log^3 n)$-competitive randomized online algorithm for this problem. We further present a randomized online algorithm which is $O(\log^2 n)$-competitive when compared to a static optimal solution. Our two results rely on different algorithms and techniques and hence are of independent interest.

翻译：许多大规模和 dataintensive 分布式系统的性能关键依赖于互连网络的容量。本文受自我调整基础设施愿景的启发，其资源可根据当前服务的工作负载进行需求感知式调整。这种动态调整可通过将频繁交互的通信伙伴动态移近（例如，将其安排在同一服务器或数据中心机架中）来优化网络利用率，进而提升性能。特别地，我们重新审视了在线平衡图划分问题，该问题刻画了动态聚合通信伙伴的收益与成本之间的基本权衡。需求建模为一个在线揭示的通信请求序列 σ，涉及 n 个进程，每个进程运行在 ℓ 台服务器中的一台。每台服务器容量为 k=n/ℓ，因此进程需在服务器间以平衡方式调度。若请求的进程位于不同服务器，则产生成本 1；否则成本为 0。进程迁移到另一台服务器的成本为 1。本文提出了首个在线平衡图划分在线算法，针对环通信模式这一基础情形实现了多对数竞争比。具体而言，我们的主要贡献是一个 O(log³ n) 竞争的随机在线算法。此外，我们提出另一个随机在线算法，相较于静态最优解具有 O(log² n) 竞争比。这两个结果依赖于不同的算法与技术，因此具有独立研究价值。