Electric power, water, natural gas and other utilities are served to consumers via functional sources such as electric power substations, pumps and pipes. Understanding the impact of service outages is vital to decision making in response and recovery efforts. Often, data pertaining to the source-sink relationships between the service points and consumers is sensitive or proprietary, and is, th...

In the paper we present purely combinatorial conditions that allow us to recognize the topological equivalence (or non-equivalence) of two given dissections. Using a computer program based on this result, we are able to generate a set which contains all topologically non-equivalent dissections of a p0-gon into convex pi-gons, i = 1, ..., n, where n, p0, ..., pn are integers such that n ≥ 2, pi ...

In this paper we study three related problems: (i) Given a fat polygon P , we show how to find a set G of points in P such that every point on the boundary of P sees at least one point of G. The set G is said to guard the boundary of P and its cardinality depends on the shape parameters of P . Fat polygons are often used to model more realistic inputs. (ii) Given k points that guard the boundar...

Introduction: The Phoenix probe landed on the northern plains of Mars (68.2°N, 234.2°E) on May 25, 2008, and the landscape seen on the first images acquired on the surface confirmed what was already known since the HiRISE camera began scrutinizing the Martian surface with unprecedented detail, that the existence of polygonal terrains is a predominant feature in that area [1][2]. The polygons ob...

We present a novel approach to the problem of generating a polygon sequence that blends two simple polygons given a correspondence between their boundaries. Previous approaches to this problem, including direct vertex interpolation and an interpolation based on edge lengths and angles between edges, tend to produce self intersections and shape distortions. Our approach introduces the star-skele...

A small polygon is a of unit diameter. The maximal area with $$n=2m$$ vertices not known when $$m\ge 7$$ . In this paper, we construct, for each and 3$$ , n-gon whose the value one-variable function. We show that, all even $$n\ge 6$$ obtained improves by $$O(1/n^5)$$ that best prior constructed Mossinghoff. particular, $$n=6$$ 6-gon has area.

Graphs have enormous usage in software engineering, network and electrical engineering. In fact graphs drawing is a geometrically representation of information. Among graphs, trees are concentrated because of their ability in hierarchical extension as well as processing VLSI circuit. Many algorithms have been proposed for drawing binary trees within polygons. However these algorithms generate b...

A convex polygon is defined as a sequence (V0, . . . , Vn−1) of points on a plane such that the union of the edges [V0, V1], . . . , [Vn−2, Vn−1], [Vn−1, V0] coincides with the boundary of the convex hull of the set of vertices {V0, . . . , Vn−1}. It is proved that all sub-polygons of any convex polygon with distinct vertices are convex. It is also proved that, if all sub-(n − 1)-gons of an n-g...

In this note we will generalize the Higman-Haemers inequalities for generalized polygons to thick regular near polygons.

We consider the multiparty communication model deened in DF89] using the formalism from Hr97]. First, we correct an inaccuracy in the proof of the fundamental result of DR95] providing a lower bound on the nondeter-ministic communication complexity of a function. Then we construct several very hard functions, i.e., functions such that those as well as their complements have the worst possible n...