A common geometric problem in computer graphics and geographic information systems is to compute the arrangement of a set of n segments that can be colored red and blue so that there are no red/red or blue/blue crossings. We give a sweep algorithm that uses the minimum arithmetic precision and runs in optimal O(n logn + k) time and O(n) space to output an arrangement with k vertices, or O(n log...

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. The class of arrangement graphs was introduced as a common generalization of star graphs and alternating group g...

We address the problem of estimating the phase φ given N copies of the phase rotation uφ within an array of quantum operations in finite dimensions. We first consider the special case where the array consists of an arbitrary input state followed by any arrangement of the N phase rotations, and ending with a POVM. We optimise the POVM for a given input state and fixed arrangement. Then we also o...

The arrangement graph An;k is not only a generalization of star graph (nÿ k ˆ 1), but also more ̄exible. In this investigation, we elucidate the problem of embedding of multiple spanning trees in an arrangement graph with the objective of congestion-free. This result is to report how to exploit 2…nÿ k† edge disjoint spanning trees in an arrangement graph, where each congestion-free spanning tre...

We present a new algorithm to compute the Legendre–Fenchel conjugate of convex piecewise linear-quadratic (PLQ) bivariate functions. The algorithm stores a function using a (primal) planar arrangement. It then computes the (dual) arrangement associated with the conjugate by looping through vertices, edges, and faces in the primal arrangement and building associated dual vertices, edges, and fac...

The order and arrangement of dimensions (variates) is crucial for the effectiveness of a large number of visualization techniques such as parallel coordinates, scatterplots, recursive pattern, and many others. In this paper, we describe a systematic approach to arrange the dimensions according to their similarity. The basic idea is to rearrange the data dimensions such that dimensions showing a...

according to the experiences gathered from pre- earthquakes & revising the rules of design bylaws the subject of reinforcing the present buildings is important nowadays. this project investigates the usage of quake system on wind- occlusion as one of the most efficient ways of shaking development in small, steel buildiongs.including important matters in studying the usage of these systems is su...