City Research Online

Abstract

We study graph augmentation under the dilation criterion. In our case, we consider a plane geometric graph 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.

Publication Type:	Article
Additional Information:	The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-45738-3
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments:	School of Science & Technology > Computer Science > giCentre
SWORD Depositor:	Symplectic Administrator

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