The spanning ratio and maximum detour of a graph G embedded in a metric space measure how well G approximates the minimum complete graph containing G and metric space, respectively. In this paper we show that computing the spanning ratio of a rectilinear path P in L1 space has a lower bound of Ω(n logn) in the algebraic computation tree model and describe a deterministic O(n log2 n) time algorithm. On the other hand, we give a deterministic O(n log2 n) time algorithm for computing the maximum detour of a rectilinear path P in L1 space and obtain an O(n) time algorithm when P is a monotone rectilinear path. © 2010 Springer-Verlag.
CITATION STYLE
Grüne, A., Lin, T. C., Yu, T. K., Klein, R., Langetepe, E., Lee, D. T., & Poon, S. H. (2010). Spanning ratio and maximum detour of rectilinear paths in the L1 plane. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6507 LNCS, pp. 121–131). https://doi.org/10.1007/978-3-642-17514-5_11
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