Approximate Euclidean shortest paths in polygonal domains

Given a set $\mathcal{P}$ of $h$ pairwise disjoint simple polygonal obstacles in $\mathbb{R}^2$ defined with $n$ vertices, we compute a sketch $\Omega$ of $\mathcal{P}$ whose size is independent of $n$, depending only on $h$ and the input parameter $\epsilon$. We utilize $\Omega$ to compute a $(1+\epsilon)$-approximate geodesic shortest path between the two given points in $O(n + h((\lg{n}) + (\lg{h})^{1+\delta} + (\frac{1}{\epsilon}\lg{\frac{h}{\epsilon}})))$ time. Here, $\epsilon$ is a user parameter, and $\delta$ is a small positive constant (resulting from the time for triangulating the free space of $\cal P$ using the algorithm in \cite{journals/ijcga/Bar-YehudaC94}). Moreover, we devise a $(2+\epsilon)$-approximation algorithm to answer two-point Euclidean distance queries for the case of convex polygonal obstacles.Comment: a few updates; accepted to ISAAC 201

Effect of therapeutic massage on pain in patients with dementia

Introduction The aim was to investigate whether therapeutic massage was effective in relieving pain in elderly residents with dementia. Methods A randomized controlled study was conducted in an aged care facility. Ten participants with dementia or advanced dementia were allocated to an intervention group or a control group. The intervention group received 10 min of massage (effleurage, kneading, and trigger point therapy) four times per week for 4 weeks. The Pain Assessment in Advanced Dementia scale was used as the outcome measure. Results No significant changes in mean outcome measure scores were found post intervention (Intervention mean = 5.0 ± 3.49; Control mean = 5.2 ± 3.49: t(8) = 0.09, p = 0.93). However, the Intervention Group had a greater magnitude of change (1.200 ± 1.78) when compared to the control group (0.800 ± 2.16). Conclusion Therapeutic massage may provide a useful adjunct to the current pain management plan of patients with dementia. </jats:sec