566 research outputs found

    Straight-line Drawability of a Planar Graph Plus an Edge

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    We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line drawing, and a linear-time drawing algorithm that constructs such a drawing, if it exists. We also show that some almost-planar graphs require exponential area for a straight-line drawing

    Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time

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    Thomassen characterized some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph is drawable in straight-lines if and only if it does not contain the configuration [C. Thomassen, Rectilinear drawings of graphs, J. Graph Theory, 10(3), 335-341, 1988]. In this paper, we characterize some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph can be re-embedded into a straight-line drawable 1-plane embedding of the same graph if and only if it does not contain the configuration. Re-embedding of a 1-plane embedding preserves the same set of pairs of crossing edges. We give a linear-time algorithm for finding a straight-line drawable 1-plane re-embedding or the forbidden configuration.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016). This is an extended abstract. For a full version of this paper, see Hong S-H, Nagamochi H.: Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time, Technical Report TR 2016-002, Department of Applied Mathematics and Physics, Kyoto University (2016

    Participant preferences for an aboriginal-specific fall prevention program: Measuring the value of culturally-appropriate care

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    © 2018 Angell et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Background Culturally-specific services are central to efforts to improve the health of Aboriginal Australians. Few empirical studies have demonstrated the value of such services relative to mainstream alternatives. Objective To assess the preferences and willingness to pay (WTP) of participants for attending a class and the relative importance of transport, cost and cultural-appropriateness in the choices made by participants. Design A discrete choice experiment (DCE) was conducted alongside a study of a culturally-specific fall-prevention service. Attributes that were assessed were out-of-pocket costs, whether transport was provided and whether the class was Aboriginal-specific. Choices of participants were modelled using panel-mixed logit methods. Results 60 patients completed the DCE. Attending a service was strongly preferred over no service (selected 99% of the time). Assuming equivalent efficacy of fall-prevention programs, participants indicated a preference for services that were culturally-specific (OR 1.25 95% CI: 1.00–1.55) and incurred lower out-of-pocket participant costs (OR 1.19 95% CI 1.11–1.27). The provision of transport did not have a statistically significant influence on service choice (p = 0.57). Discussion and conclusions This represents the first published DCE in the health field examining preferences amongst an Aboriginal population. The results empirically demonstrate the value of the culturally-specific element of a program has to this cohort and the potential that stated-preference methods can have in incorporating the preferences of Aboriginal Australians and valuing cultural components of health services. Note on terminology As the majority of the NSW Aboriginal and Torres Strait Islander population is Aboriginal (97.2%), this population will be referred to as ‘Aboriginal’ in this manuscript
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