Graphs with Plane Outside-Obstacle Representations

An \emph{obstacle representation} of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent. Obstacle representations are a recent generalization of classical polygon--vertex visibility graphs, for which the characterization and recognition problems are long-standing open questions. In this paper, we study \emph{plane outside-obstacle representations}, where all obstacles lie in the unbounded face of the representation and no two visibility segments cross. We give a combinatorial characterization of the biconnected graphs that admit such a representation. Based on this characterization, we present a simple linear-time recognition algorithm for these graphs. As a side result, we show that the plane vertex--polygon visibility graphs are exactly the maximal outerplanar graphs and that every chordal outerplanar graph has an outside-obstacle representation.Comment: 12 pages, 7 figure

Hamiltonian orthogeodesic alternating paths

AbstractLet R be a set of red points and let B be a set of blue points. The point set P=R∪B is called equitable if ||B|−|R||⩽1 and it is called general if no two points are vertically or horizontally aligned. An orthogeodesic alternating path on P is a path such that each edge is an orthogeodesic chain connecting points of different color and such that no two edges cross. We consider the problem of deciding whether a set of red and blue points admits a Hamiltonian orthogeodesic alternating path, that is, an orthogeodesic alternating path visiting all points. We prove that every general equitable point set admits a Hamiltonian orthogeodesic alternating path and we present an O(nlog2n)-time algorithm for finding such a path, where n is the number of points. On the other hand, we show that the problem is NP-complete if the path must be on the grid (i.e., vertices and bends have integer coordinates). Further, we show that we can approximate the maximum length of an orthogeodesic alternating path on the grid by a factor of 3, whereas we present a family of point sets with n points that do not have a Hamiltonian orthogeodesic alternating path with more than n/2+2 points. Additionally, we show that it is NP-complete to decide whether a given set of red and blue points on the grid admits an orthogeodesic perfect matching if horizontally aligned points are allowed. This contrasts a recent result by Kano (2009) [9] who showed that this is possible on every general point set

Socio-economic impacts - forestry and agriculture

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Refining Critical Structure Contouring in STereotactic Arrhythmia Radioablation (STAR): Benchmark Results and Consensus Guidelines from the STOPSTORM.eu Consortium.

BACKGROUND AND PURPOSE In patients with recurrent ventricular tachycardia (VT), STereotactic Arrhythmia Radioablation (STAR) shows promising results. The STOPSTORM consortium was established to investigate and harmonise STAR treatment in Europe. The primary goals of this benchmark study were to standardise contouring of organs at risk (OAR) for STAR, including detailed substructures of the heart, and accredit each participating centre. MATERIALS AND METHODS Centres within the STOPSTORM consortium were asked to delineate 31 OAR in three STAR cases. Delineation was reviewed by the consortium expert panel and after a dedicated workshop feedback and accreditation was provided to all participants. Further quantitative analysis was performed by calculating DICE similarity coefficients (DSC), median distance to agreement (MDA), and 95th percentile distance to agreement (HD95). RESULTS Twenty centres participated in this study. Based on DSC, MDA and HD95, the delineations of well-known OAR in radiotherapy were similar, such as lungs (median DSC=0.96, median MDA=0.1mm and median HD95=1.1mm) and aorta (median DSC=0.90, median MDA=0.1mm and median HD95=1.5mm). Some centres did not include the gastro-oesophageal junction, leading to differences in stomach and oesophagus delineations. For cardiac substructures, such as chambers (median DSC=0.83, median MDA=0.2mm and median HD95=0.5mm), valves (median DSC=0.16, median MDA=4.6mm and median HD95=16.0mm), coronary arteries (median DSC=0.4, median MDA=0.7mm and median HD95=8.3mm) and the sinoatrial and atrioventricular nodes (median DSC=0.29, median MDA=4.4mm and median HD95=11.4mm), deviations between centres occurred more frequently. After the dedicated workshop all centres were accredited and contouring consensus guidelines for STAR were established. CONCLUSION This STOPSTORM multi-centre critical structure contouring benchmark study showed high agreement for standard radiotherapy OAR. However, for cardiac substructures larger disagreement in contouring occurred, which may have significant impact on STAR treatment planning and dosimetry evaluation. To standardize OAR contouring, consensus guidelines for critical structure contouring in STAR were established