The straight skeleton of a simple polygon is defined as the trace of the vertices when the initial polygon is shrunken in self-parallel manner [2]. In this paper, we propose a simple algorithm for drawing the straight skeleton of a monotone polygon. The time and space complexities of our algorithm are O(nlogn) and O(n) respectively.

We show that the maximum number of convex polygons in a triangulation of n points in the plane is O(1.5029). This improves an earlier bound of O(1.6181) established by van Kreveld, Löffler, and Pach (2012) and almost matches the current best lower bound of Ω(1.5028) due to the same authors. Given a planar straight-line graph G with n vertices, we also show how to compute efficiently the number ...

For any planar straight line graph (Pslg), there is a vertexface assignment such that every vertex is assigned to at most two incident faces, and every face is assigned to all its reflex vertices and one more incident vertex. The existence of such an assignment implies, in turn, that any Pslg can be augmented to a connected Pslg such that the degree of every vertex increases by at most two.

The key to successful long-term peritoneal dialysis (PD) is permanent and safe access to peritoneal cavity. The two most commonly used Tenckoff catheters for PD are the straight and coiled catheters. The present study was undertaken to assess the catheter survival, catheter associated infections, and all cause mortality and to compare the straight with coiled catheters in PD. During April 1997-...

With rising trading volumes in domestic and cross-border security transactions, risks faced by global financial firms and markets are increasing. To manage settlement risks and maintain competitiveness in global financial markets, the U.S. Security and Exchange Commission (SEC) has decided to shorten the settlement cycle of security transactions from the current T+3 to T+1. As a result, key pla...

Let G be a cycle-free connected straight-line graph with predefined edge lengths and fixed order of incident edges around each vertex. We address the problem of deciding whether there exists a simple polygon P such that G is the straight skeleton of P . We show that for given G such a polygon P might not exist, and if it exists it might not be unique. For the later case we give an example with ...