Polygon scheduling

Isotopic equivalence by Bézier curve subdivision for application to high performance computing

For an arbitrary degree Bézier curve B, we first establish sufficient conditions for its control polygon to become homeomorphic to B via subdivision. This is extended to show a subdivided control polygon that is ambient isotopic to B. We provide closed-form formulas to compute the corresponding number of iterations for equivalence under homeomorphism and ambient isotopy. The development of thes...

The 3-dimensional searchlight scheduling problem

The problem of searching for a mobile intruder in a polygonal region by a set of stationary guards, each carrying an orientable laser, is known in the literature as the Searchlight Scheduling Problem. A long-standing conjecture concerns the NP-hardness of deciding if a given polygon is searchable by a given set of guards. In this paper we introduce the more general problem of detecting an intru...

Ranking efficient units by regular polygon area in DEA

Hybrid Genetic Tabu Search for a Cyclic Scheduling Problem

This paper considers a cyclic scheduling problem, which especially is applicable in the area of public transport. The problem is the so-called Irregular Polygon Scheduling Problem with the objective to maximize the distance between the nearest vertices of two different polygons. We give a mixed integer LP-formulation of this NP-hard problem, derive some bounds and present a hybrid meta-heuristi...

Algorithm for finding the largest inscribed rectangle in polygon

In many industrial and non-industrial applications, it is necessary to identify the largest inscribed rectangle in a certain shape. The problem is studied for convex and non-convex polygons. Another criterion is the direction of the rectangle: axis aligned or general. In this paper a heuristic algorithm is presented for finding the largest axis aligned inscribed rectangle in a general polygon. ...

Points at Rational Distance from the Vertices of a Unit Polygon