conference paper
Partitioned neighborhood spanners of minimal outdegree
Matthias
Fischer
author 146
Tamas
Lukovszki
author
Martin
Ziegler
author
63
department
A geometric spanner with vertex set P in Rd is a sparse approximation of the complete Euclidean graph determined by P. We introduce the notion of partitioned neighborhood graphs (PNGs), unifying and generalizing most constructions of spanners treated in literature. Two important parameters characterizing their properties are the outdegree k in N and the stretch factor f>1 describing the quality of approximation. PNGs have been throughly investigated with respect to small values of f. We present in this work results about small values of k. The aim of minimizing k rather than f arises from two observations:
* k determines the amount of space required for storing PNGs.
* Many algorithms employing a (previously constructed) spanner have running times depending on its outdegree.
Our results include, for fixed dimensions d as well as asymptotically, upper and lower bounds on this optimal value of k. The upper bounds are shown constructively and yield efficient algorithms for actually computing the corresponding PNGs even in degenerate cases.
https://ris.uni-paderborn.de/download/17864/18438/hni-id-729.pdf
application/pdf
1999
eng
Proceedings of the 11th Canadian Conference on Computational Geometry
http://www.cccg.ca/proceedings/1999/fp36.pdf
Fischer, M., Lukovszki, T., & Ziegler, M. (1999). Partitioned neighborhood spanners of minimal outdegree. In <i>Proceedings of the 11th Canadian Conference on Computational Geometry</i>. Vancouver.
Fischer, Matthias, Tamas Lukovszki, and Martin Ziegler. “Partitioned Neighborhood Spanners of Minimal Outdegree.” In <i>Proceedings of the 11th Canadian Conference on Computational Geometry</i>. Vancouver, 1999.
M. Fischer, T. Lukovszki, M. Ziegler, in: Proceedings of the 11th Canadian Conference on Computational Geometry, Vancouver, 1999.
@inproceedings{Fischer_Lukovszki_Ziegler_1999, place={Vancouver}, title={Partitioned neighborhood spanners of minimal outdegree}, booktitle={Proceedings of the 11th Canadian Conference on Computational Geometry}, author={Fischer, Matthias and Lukovszki, Tamas and Ziegler, Martin}, year={1999} }
M. Fischer, T. Lukovszki, and M. Ziegler, “Partitioned neighborhood spanners of minimal outdegree,” in <i>Proceedings of the 11th Canadian Conference on Computational Geometry</i>, 1999.
Fischer, Matthias, et al. “Partitioned Neighborhood Spanners of Minimal Outdegree.” <i>Proceedings of the 11th Canadian Conference on Computational Geometry</i>, 1999.
Fischer M, Lukovszki T, Ziegler M. Partitioned neighborhood spanners of minimal outdegree. In: <i>Proceedings of the 11th Canadian Conference on Computational Geometry</i>. Vancouver; 1999.
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