@article{1583,
abstract = {We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon.},
author = {Biedl, Therese and Held, Martin and Huber, Stefan and Kaaser, Dominik and Palfrader, Peter},
journal = {Information Processing Letters},
number = {2},
pages = {243 -- 247},
publisher = {Elsevier},
title = {{A simple algorithm for computing positively weighted straight skeletons of monotone polygons}},
doi = {10.1016/j.ipl.2014.09.021},
volume = {115},
year = {2015},
}
@article{1584,
abstract = {We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.},
author = {Biedl, Therese and Held, Martin and Huber, Stefan and Kaaser, Dominik and Palfrader, Peter},
journal = {Computational Geometry: Theory and Applications},
number = {5},
pages = {429 -- 442},
publisher = {Elsevier},
title = {{Reprint of: Weighted straight skeletons in the plane}},
doi = {10.1016/j.comgeo.2015.01.004},
volume = {48},
year = {2015},
}
@inbook{1590,
abstract = {The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.},
author = {Aichholzer, Oswin and Biedl, Therese and Hackl, Thomas and Held, Martin and Huber, Stefan and Palfrader, Peter and Vogtenhuber, Birgit},
booktitle = {Graph Drawing and Network Visualization},
location = {Los Angeles, CA, United States},
pages = {335 -- 347},
publisher = {Springer},
title = {{Representing directed trees as straight skeletons}},
doi = {10.1007/978-3-319-27261-0_28},
volume = {9411},
year = {2015},
}
@article{1816,
abstract = {Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques.},
author = {Huber, Stefan and Held, Martin and Meerwald, Peter and Kwitt, Roland},
journal = {International Journal of Computational Geometry and Applications},
number = {1},
pages = {61 -- 86},
publisher = {World Scientific Publishing},
title = {{Topology-preserving watermarking of vector graphics}},
doi = {10.1142/S0218195914500034},
volume = {24},
year = {2014},
}
@article{1842,
abstract = {We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by O(n3) and O(n10), in the convex and general case, respectively. We then apply similar methods to prove an (Formula presented.) upper bound on the Ramsey number of a path with n ordered vertices.},
author = {Cibulka, Josef and Gao, Pu and Krcál, Marek and Valla, Tomáš and Valtr, Pavel},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {64 -- 79},
publisher = {Springer},
title = {{On the geometric ramsey number of outerplanar graphs}},
doi = {10.1007/s00454-014-9646-x},
volume = {53},
year = {2014},
}