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

Computing a rectilinear shortest path amid splinegons in plane

We reduce the problem of computing a rectilinear shortest path between two given points s and t in the splinegonal domain \calS to the problem of computing a rectilinear shortest path between two points in the polygonal domain. As part of this, we define a polygonal domain \calP from \calS and transform a rectilinear shortest path computed in \calP to a path between s and t amid splinegon obstacles in \calS. When \calS comprises of h pairwise disjoint splinegons with a total of n vertices, excluding the time to compute a rectilinear shortest path amid polygons in \calP, our reduction algorithm takes O(n + h \lg{n}) time. For the special case of \calS comprising of concave-in splinegons, we have devised another algorithm in which the reduction procedure does not rely on the structures used in the algorithm to compute a rectilinear shortest path in polygonal domain. As part of these, we have characterized few of the properties of rectilinear shortest paths amid splinegons which could be of independent interest

New Northwestern and Southwestern Range Limits of De Brazza's Monkey, Mbam Et Djerem National Park, Cameroon, and Bateke Plateau, Gabon and Congo

Recent surveys carried out in Cameroon in the Mbam Djerem National Park, in Gabon in the Bateke Plateau National Park, and the adjoining Bateke Plateau area, in Congo, have recorded the presence of De Brazza's monkey Cercopithecus neglectus on both sides of the Djerem River in Cameroon, along the Mpassa and its tributaries in Gabon, along the Nambouli River in the Lefini Reserve in Congo, and up to the right bank of the Ogooué River on the Congo side of the border. These areas lie at the northern and southern edges of the Central African forest block, where rivers have relatively wide bands of riparian forest. As for the range extension of the talapoin (this volume), the species may simply have been overlooked by previous rapid wildlife surveys. It has an antipredator behavior that renders it relatively inconspicuous, tends to live in small family groups in the region, and lives in habitats that are difficult to survey on foot. However, unlike talapoin, it calls every morning along major watercourses, and can be heard for some distance. It is possible that the southern limit of this species in Gabon may be the Ogooué River. Future survey teams are encouraged to familiarize themselves with the long call of this species and to be aware that it can occur in gallery forests throughout the savannas of the Bateke Plateau and also in the area between the Mbam, the Djerem, and the Lom in Cameroon.; Les recensements récents au Cameroun dans le parc national de Mbam et Djerem, au Gabon dans le parc national de Plateau Bateke et dans les savanes Bateke avoisinante au Congo ont notée la présence du singe de Brazza Cercopithecus neglectus sur les deux rives du Djerem au Cameroun, le long de l'Mpassa et ses tributaires au Gabon, le long de la rivière Nambouli dans la Reserve de la Lefini au Congo, et jusqu'au rive droite de la rivière Ogooué sur la coté Congolaise de la frontière. Les deux zones se trouvent aux bords nord et sud du grand bloc forestier du bassin du Congo, et contiennent les rivières importantes, qui coulent dans les galeries assez larges de foret ripicole. Comme pour les talapoins (ce volume), l'espèce a été peutêtre simplement ratée par les équipes de recensement dans la région auparavant. Il a un comportement anti-prédateur qui le rend très discret, une tendance � vivre par petits groupes familiaux, difficiles � repérer, de plus occupe un habitat plus difficilement accessible � un observateur � pied les habitats de la plupart des autres guenons. Néanmoins, et contrairement au comportement des talapoins, chaque matin il pousse des cris très caractéristiques, audible sur des grandes distances le long des grandes rivières. Il est possible que la limite sud de cette espèce au Gabon soit la rivière Ogooué. Les équipes de recensement de la faune sont encouragées de se familiarisée avec les vocalisations de cette espèce, et garder � l'esprit que le singe de Brazza peut être présent dans les forets galeries dans toutes les savanes du plateaux Batéké et aussi, au Cameroun, la zone entre les rivières Mbam, Djerem, et Lom