Abstract
A t-spanner is a graph on a set of points S with the following property: Between any pair of points there is a path in the spanner whose total length is at most t times the actual distance between the points. In this paper, we consider points residing in a metric space equipped with doubling dimension λ, and show how to construct a dynamic (1 + ε)-spanner with degree ε − O(λ) in \(O(\frac{\log n}{\varepsilon^{O(\lambda)}})\) update time. When λ and ε are taken as constants, the degree and update times are optimal.
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Gottlieb, LA., Roditty, L. (2008). An Optimal Dynamic Spanner for Doubling Metric Spaces. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_40
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DOI: https://doi.org/10.1007/978-3-540-87744-8_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87743-1
Online ISBN: 978-3-540-87744-8
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