Local Routing in Spanners Based on WSPDs

Bose, Prosenjit; Carufel, Jean-Lou De; Dujmović, Vida; Paradis, F.

doi:10.1007/978-3-319-62127-2_18

Cited by 3 publications

(5 citation statements)

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“…This article considers the local routing problem on (1 + ε)-spanners constructed from a WSPD. A few routing algorithms for this problem have been previously proposed [7,3]. All achieve a 1 + O(1/s) routing ratio, where s is the parameter used in the WSPD construction.…”

Section: Related Workmentioning

confidence: 99%

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Routing on Heavy-Path WSPD-Spanners

Bose

Tuttle

2021

Lecture Notes in Computer Science

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In this article, we present a construction of a spanner on a set of n points in R d that we call a heavy path WSPD spanner. The construction is parameterized by a constant s > 2 called the separation ratio. The size of the graph is O(s d n) and the spanning ratio is at most 1 + 2/s + 2/(s − 1). We also show that this graph has a hop spanning ratio of at most 2 lg n + 1.We present a memoryless local routing algorithm for heavy path WSPD spanners. The routing algorithm requires a vertex v of the graph to store O(deg(v) log n) bits of information, where deg(v) is the degree of v. The routing ratio is at most 1 + 4/s + 1/(s − 1) and at least 1 + 4/s in the worst case. The number of edges on the routing path is bounded by 2 lg n + 1.We then show that the heavy path WSPD spanner can be constructed in metric spaces of bounded doubling dimension. These metric spaces have been studied in computational geometry as a generalization of Euclidean space. We show that, in a metric space with doubling dimension λ, the heavy path WSPD spanner has size O(s λ n) where s is the separation ratio. The spanning ratio and hop spanning ratio are the same as in the Euclidean case.Finally, we show that the local routing algorithm works in the bounded doubling dimension case. The vertices require the same amount of storage, but the routing ratio becomes at most 1 + (2 + τ τ −1 )/s + 1/(s − 1) in the worst case, where τ ≥ 11 is a constant related to the doubling dimension.Proposition 1.1 (28, Proposition 3). Let (X, d) and (Y, δ) be metric spaces such that the doubling dimension of X is λ. Suppose there is a bijectionCorollary 1.2. Let G be a t-spanner constructed in a metric space with doubling dimension λ. Then the doubling dimension of the shortest path metric on G is at most 4λ⌈lg(4t)⌉.

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Section: Related Workmentioning

confidence: 99%

“…The first algorithms for routing on WSPD spanners appeared in Bose et al [7]. They propose two algorithms, a 2-local and a 1-local routing algorithm.…”

Section: Related Workmentioning

confidence: 99%

Routing on Heavy-Path WSPD-Spanners

Bose

Tuttle

2021

Lecture Notes in Computer Science

Self Cite

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show abstract

“…This thesis considers the local routing problem on (1 + ε)-spanners constructed from a WSPD. A few routing algorithms for this problem have been previously proposed [8,4]. All achieve a 1 + O(1/s) routing ratio, where s is the parameter used in the WSPD construction.…”

Section: Related Workmentioning

confidence: 99%

“…The first algorithms for routing on WSPD spanners appeared in Bose et al [8]. They propose two algorithms, a 2-local and a 1-local routing algorithm.…”

Section: Related Workmentioning

confidence: 99%