Self-adjusting Linear Networks

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 tradeoff: 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 Ω(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.We presented a first and asymptotically tight, i.e., Θ(log n)-competitive online algorithm for self-adjusting reconfigurable line networks with linear demand. Both our lower and upper bounds are non-trivial, and we believe that our work opens several interesting directions for future research. In particular, it would be very interesting to shed light on the competitive ratio achievable in more general network topologies, and to study randomized algorithms.

Self-Adjusting Linear Networks with Ladder Demand Graph

“…Let us talk a little bit about the previous results from [1]. In that work, the demand graph was the line graph L n , as the network graph.…”

“…In the previous work [1], the demand graph is also a line. The authors presented an algorithm that serves m " Ωpn 2 q requests at cost Opn 2 log n `mq and showed that this complexity is the lower bound.…”

“…The problem is inspired by Itinerant List Update Problem [14]. To be more precise, the problem in [1] appears to be the restricted version of online Dynamic Minimum Linear Arrangement 1 problem, which is another reformulation of ILU. We need to note that in [14] offline algorithms were considered while we consider online versions in this paper.…”

“…Their formal representations are introduced in [6], [16]. Existing works have studied linear networks [1], bounded degree networks [7], skip list networks [5] and skip graphs [13]. Moreover, recent work has also focused in more advanced cost models [2], [9].…”

“…Moreover, recent work has also focused in more advanced cost models [2], [9]. The most relevant work to ours [1] studied linear networks with linear demand graphs. Furthermore, [4] studied optimal network topologies, when the demand is known.…”