# Self-Adjusting Linear Networks

## TL;DR

This paper studies self-adjusting linear networks that dynamically reconfigure to workload demands, balancing reconfiguration costs and performance, and provides theoretical bounds and algorithms for their online optimization.

## Contribution

It introduces a formal model for demand-aware self-adjusting linear networks and analyzes their algorithmic complexity and competitive performance.

## Key findings

- Established an $oldsymbol{ ext{Ω}( ext{log}n)}$ lower bound on competitive ratio.
- Developed an $oldsymbol{O( ext{log}n)}$-competitive online algorithm for ordered requests.
- Showed the problem generalizes the classic dynamic list update problem.

## Abstract

Emerging networked systems become increasingly flexible and reconfigurable. 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 trade-off: while more frequent adjustments can improve performance, they also entail higher reconfiguration costs. This paper initiates the formal study of linear networks which self-adjust to the demand in an online manner, striking a balance between the benefits and costs of reconfigurations. We show that the underlying algorithmic problem can be seen as a distributed generalization of the classic dynamic list update problem known from self-adjusting datastructures: in a network, requests can occur between node pairs. This distributed version turns out to be significantly harder than the classical problem in generalizes. Our main results are a $\Omega(\log{n})$ lower bound on the competitive ratio, and a (distributed) online algorithm that is $O(\log{n})$-competitive if the communication requests are issued according to a linear order.