While operating communication networks adaptively may improve utilization and performance, frequent adjustments also introduce an algorithmic challenge: the re-optimization of traffic engineering solutions is time-consuming and may limit the granularity at which a network can be adjusted. This paper is motivated by question whether the reactivity of a network can be improved by re-optimizing solutions dynamically rather than from scratch, especially if inputs such as link weights do not change significantly. This paper explores to what extent dynamic algorithms can be used to speed up fundamental tasks in network operations. We specifically investigate optimizations related to traffic engineering (namely shortest paths and maximum flow computations), but also consider spanning tree and matching applications. While prior work on dynamic graph algorithms focuses on link insertions and deletions, we are interested in the practical problem of link weight changes. We revisit existing upper bounds in the weight-dynamic model, and present several novel lower bounds on the amortized runtime for recomputing solutions. In general, we find that the potential performance gains depend on the application, and there are also strict limitations on what can be achieved, even if link weights change only slightly.

翻译：虽然自适应地运行通信网络可以提高利用率和性能，但频繁调整也带来了算法挑战：流量工程解决方案的重新优化非常耗时，并可能限制网络调整的粒度。本文的动机源于一个问题：能否通过动态重新优化而非从头开始优化来改善网络的响应性，尤其是在链路权重等输入变化不大时。本文探索了动态算法在多大程度上可用于加速网络运营中的基本任务。我们特别研究了与流量工程相关的优化问题（即最短路径和最大流计算），同时也考虑了生成树和匹配应用。虽然先前关于动态图算法的工作侧重于链路的插入和删除，但我们关注的是链路权重变化的实际工程问题。我们重新审视了现有权重动态模型中的上界，并为重新计算解决方案的均摊运行时间提出了若干新颖的下界。总体而言，我们发现潜在的性能提升取决于具体应用，并且即使链路权重仅发生微小变化，所能取得的成果也存在严格限制。