Abstract
A geometric t-spanner on a set of points in Euclidean space is a graph containing for every pair of points a path of length at most t times the Euclidean distance between the points. Informally, a spanner is O(k)-robust if deleting k vertices only harms O(k) other vertices. We show that on any one-dimensional set of n points, for any ε>0, there exists an O(k)-robust 1-spanner with O(n1+ε) edges. Previously it was only known that O(k)-robust spanners with O(n2) edges exists and that there are point sets on which any O(k)-robust spanner has Ω(nlogn) edges.
Original language | English |
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Publisher | Cornell university |
Number of pages | 6 |
Publication status | Published - 2018 |
Keywords
- Computational Geometry