2014
DOI: 10.1137/130945636
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Computing the Stretch of an Embedded Graph

Abstract: Let G be a graph embedded in an orientable surface Σ, possibly with edge weights, and denote by len(γ) the length (the number of edges or the sum of the edge weights) of a cycle γ in G. The stretch of a graph embedded on a surface is the minimum of len(α) • len(β) over all pairs of cycles α and β that cross exactly once. We provide an algorithm to compute the stretch of an embedded graph in time O(g 4 n log n) with high probability, or in time O(g 4 n log 2 n) in the worst case, where g is the genus of the sur… Show more

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Cited by 1 publication
(3 citation statements)
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“…In the quest for another embedding density parameter suitable for capturing the two-dimensional character of the toroidal expanse and crossing number problems, we put forward the following concept improving upon the original "orthogonal width" of [20]. We remark in passing that although our paper does not use nor provide an algorithm to compute the stretch of an embedding, this can be done efficiently on any surface by [6].…”
Section: Stretch Of An Embedded Graphmentioning
confidence: 99%
See 2 more Smart Citations
“…In the quest for another embedding density parameter suitable for capturing the two-dimensional character of the toroidal expanse and crossing number problems, we put forward the following concept improving upon the original "orthogonal width" of [20]. We remark in passing that although our paper does not use nor provide an algorithm to compute the stretch of an embedding, this can be done efficiently on any surface by [6].…”
Section: Stretch Of An Embedded Graphmentioning
confidence: 99%
“…We remark in passing that although our paper does not use nor provide an algorithm to compute the stretch of an embedding, this can be done efficiently on any surface by [6].…”
Section: Stretch Of An Embedded Graphmentioning
confidence: 99%
See 1 more Smart Citation