On the Complexity of Weight-Dynamic Network Algorithms

TL;DR

This paper investigates the potential and limitations of dynamic algorithms for traffic engineering tasks in communication networks, focusing on link weight changes and their impact on re-optimization efficiency.

Contribution

It revisits existing bounds and introduces new lower bounds for weight-dynamic algorithms, highlighting application-dependent performance gains and inherent limitations.

Findings

Performance gains vary by application

Strict limitations exist even with small weight changes

New lower bounds on amortized runtime for re-optimization

Abstract

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.