An Optimal Algorithm for Computing Visibility in the Plane

An Optimal Algorithm for Computing the Spherical Depth of Points in the Plane

For a distribution function F on R and a point q ∈ R, the spherical depth SphD(q;F ) is defined to be the probability that a point q is contained inside a random closed hyper-ball obtained from a pair of points from F . The spherical depth SphD(q;S) is also defined for an arbitrary data set S ⊆ R and q ∈ R. This definition is based on counting all of the closed hyper-balls, obtained from pairs ...

An Optimal Algorithm for Euclidean Shortest Paths in the Plane

We propose an optimal-time algorithm for a classical problem in plane computational geometry: computing a shortest path between two points in the presence of polygonal obstacles. Our algorithm runs in worst-case time O(n logn) and requires O(n logn) space, where n is the total number of vertices in the obstacle polygons. The algorithm is based on an eecient implementation of wavefront propagati...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Width-Optimal Visibility Representations of Plane Graphs

An Optimal Algorithm Computing Edge-to-Edge Visibility in a Simple Polygon

Let P be a simple polygon with n vertices. We present a new O(n)-time algorithm to compute the visible part of one edge from another edge of P . The algorithm does not alter the input and only uses O(1) variables and is therefore a constant-workspace algorithm. The algorithm can be used to make a constant-workspace algorithm for computing the weak visibility polygon from an edge in O(mn) time, ...