Partitioning polygons via graph augmentation

Jan-Henrik Haunert, Wouter Meulemans

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

3 Citations (Scopus)
9 Downloads (Pure)

Abstract

We study graph augmentation under the dilation criterion. In our case, we consider a plane geometric graph G=(V,E)
G=(V,E)
and a set C of edges. We aim to add to G a minimal number of nonintersecting edges from C to bound the ratio between the graph-based distance and the Euclidean distance for all pairs of vertices described by C. Motivated by the problem of decomposing a polygon into natural subregions, we present an optimal linear-time algorithm for the case that P is a simple polygon and C models an internal triangulation of P. The algorithm admits some straightforward extensions. Most importantly, in pseudopolynomial time, it can approximate a solution of minimum total length or, if C is weighted, compute a solution of minimum total weight. We show that minimizing the total length or the total weight is weakly NP-hard.

Finally, we show how our algorithm can be used for two well-known problems in GIS: generating variable-scale maps and area aggregation.
Original languageEnglish
Title of host publicationGeographic Information Science
Subtitle of host publication9th International Conference, GIScience 2016, Montreal, QC, Canada, September 27-30, 2016, Proceedings
EditorsJ.A. Miller, D. O'Sullivan, N. Wiegand
Place of PublicationDordrecht
PublisherSpringer
Pages18-33
ISBN (Electronic)978-3-319-45738-3
ISBN (Print)978-3-319-45737-6
DOIs
Publication statusPublished - 2016
Externally publishedYes

Publication series

NameLecture Notes in Computer Science
Volume9927

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