Given a set of n points S in the plane, a triangulation T of S is a maximal set of non-crossing segments with endpoints in S. We present an algorithm that computes the number of triangulations on a given set of n points in time n √ , significantly improving the previous best running time of O(2n) by Alvarez and Seidel [SoCG 2013]. Our main tool is identifying separators of size O( √ n) of a tri...

In the oil industry, huge saving may be made if suitable multi-interface level measurement systems are employed for effectively monitoring crude oil separators and efficient control of their operation. A number of techniques, e.g. externally mounted displacers, differential pressure transmitters and capacitance rod devices, have been developed to measure the separation process with gas, oil, wa...

A scheme is presented for mapping the connectivity of a potential magnetic field arising from an arbitrary distribution of discrete sources. The field lines interconnecting the sources are classified into Nd domains, defining the field’s connectivity. The number of domains is shown to depend on the number of sources and on the numbers of nulls and separators according to a simple relation. A cl...

In this paper, we analyze ptolemaic graphs for its properties as chordal graphs. Firstly, two characterizations of ptolemaic graphs are proved. The first one is based on the reduced clique graph, a structure that was defined by Habib and Stacho [8]. In the second one, we simplify the characterization presented by Uehara and Uno [13] with a new proof. Then, known subclasses of ptolemaic graphs a...