Grid spanners with low forwarding index for energy efficient networks

Giroire, Frédéric; Pérennès, Stéphane; Tahiri, Issam

doi:10.1016/j.dam.2017.02.021

Cited by 1 publication

(2 citation statements)

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“…We now study graphs with a constraint on the degree (∆ will denote the maximum degree). The motivation comes from telecommunication & real interconnection networks for which the node degree is often small, see for example [19,8].…”

Section: Minimally Congested Graphsmentioning

confidence: 99%

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How to Design Graphs with Low Forwarding Index and Limited Number of Edges

Giroire

Pérennès

Tahiri

2016

Lecture Notes in Computer Science

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The (edge) forwarding index of a graph is the minimum, over all possible routings of all the demands, of the maximum load of an edge. This metric is of a great interest since it captures the notion of global congestion in a precise way: the lesser the forwardingindex, the lesser the congestion. In this paper, we study the following design question: Given a number e of edges and a number n of vertices, what is the least congested graph that we can construct? and what forwarding-index can we achieve? Our problem has some distant similarities with the well-known (∆, D) problem, and we sometimes build upon results obtained on it. The goal of this paper is to study how to build graphs with low forwarding indices and to understand how the number of edges impacts the forwarding index. We answer here these questions for different families of graphs: general graphs, graphs with bounded degree, sparse graphs with a small number of edges by providing constructions, most of them asymptotically optimal. For instance, we provide an asymptotically optimal construction for (n, n + k) cubic graphs-its forwarding index is ∼ n 2 3k log 2 (k). Our results allow to understand how the forwarding-index drops when edges are added to a graph and also to determine what is the best (i.e least congested) structure with e edges. Doing so, we partially answer the practical problem that initially motivated our work: If an operator wants to power only e links of its network, in order to reduce the energy consumption (or wiring cost) of its networks, what should be those links and what performance can be expected?

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Section: Minimally Congested Graphsmentioning

confidence: 99%

“…Here is an example. When restricted to the class of cubic graphs, the min congested (8,12)graph is the cube. Its forwarding index is equal to 8.…”

Section: Introductionmentioning

confidence: 99%