Local Routing in a Tree Metric 1-Spanner

Brankovic, Milutin; Gudmundsson, Joachim; Renssen, André van

doi:10.1007/978-3-030-58150-3_14

Cited by 3 publications

(1 citation statement)

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“…Euclidean spanners of bounded degree have been studied since the early 90s, and they too found various applications. In compact routing schemes low degree spanners give rise to routing tables of small size (see, e.g., [18,49,15]), and more generally, the degree of the spanner determines the local memory constraints when using spanners also for other purposes, such as constructing network synchronizers and efficient broadcast protocols. Moreover, in some applications the degree of a vertex (or processor) represents its load, hence a low degree spanner guarantees that the load on all the processors in the network will be low.…”

Section: Introductionmentioning

confidence: 99%

Towards a Unified Theory of Light Spanners I: Fast (Yet Optimal) Constructions

Le¹,

Solomon²

2021

Preprint

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Seminal works on light spanners over the years provide spanners with optimal or near-optimal lightness in various graph classes, such as in general graphs [21], Euclidean spanners [33] and minorfree graphs [12]. Two shortcomings of all previous work on light spanners are: (1) The techniques are ad hoc per graph class, and thus can't be applied broadly (e.g., some require large stretch and are thus suitable to general graphs, while others are naturally suitable to stretch 1 + ). ( 2) The runtimes of these constructions are almost always sub-optimal, and usually far from optimal.This work aims at initiating a unified theory of light spanners by presenting a single framework that can be used to construct light spanners in a variety of graph classes. This theory is developed in two papers. The current paper is the first of the two -it lays the foundations of the theory of light spanners and then applies it to design fast constructions with optimal lightness for several graph classes. Our new constructions are significantly faster than the state-of-the-art for every examined graph class; moreover, our runtimes are near-linear and usually optimal.Specifically, this paper includes the following results (for simplicity assume > 0 is fixed):Remark. Our follow-up paper builds on the foundations of the theory laid in the current paper, aiming to achieve lightness bounds with optimal dependencies on the involved parameters, most notably , but also others such as the dimension (in Euclidean spaces) or the minor size (in minor-free graphs).

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Section: Introductionmentioning

confidence: 99%