Geometric spanners with few edges and degree five

Authors:
Michiel Smid
Affiliations:
School of Computer Science, Carleton University, Ottawa, Ontario, Canada
Venue:
CATS '06 Proceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 51
Year:
2006

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Abstract

An O(n log n)-time algorithm is presented that, when given a set S of n points in Rd and an integer k with 0 ≤ k ≤ n, computes a graph with vertex set S, that contains at most n - 1 + k edges, has stretch factor O(n/(k+1), and whose degree is at most five. This generalizes a recent result of Aronov et al., who obtained this result for two-dimensional point sets.