António Leslie Bajuelos

A Methodology for Developing Adaptive Educational-Game Environments

In this paper we present a methodology for describing adaptive educational-game environments and a model that supports the environment design process. These environments combine the advantages of educational games with those derived from the adaptation. The proposed methodology allows the specification of educational methods that can be used for the game environment generation. The educational goals, the activities that the users can perform, their organization and sequencing, along with the games to be played and the game stories are selected or dynamically generated taking into account the users features and behaviors.

Quadratic-Time Linear-Space Algorithms for Generating Orthogonal Polygons with a Given Number of Vertices

We propose Inflate-Paste – a new technique for generating orthogonal polygons with a given number of vertices from a unit square based on gluing rectangles. It is dual to Inflate-Cut – a technique we introduced in [12] that works by cutting rectangles.

Approximation algorithms to minimum vertex cover problems on polygons and terrains

We propose an anytime algorithm to compute successively better approximations of the optimum of Minimum Vertex Guard. Though the presentation is focused on polygons, the work may be directly extended to terrains along the lines of [4]. A major idea in our approach is to explore dominance of visibility regions to first detect pieces that are more difficult to guard.

Generating Random Orthogonal Polygons

We propose two different methods for generating random orthogonal polygons with a given number of vertices. One is a polynomial time algorithm and it is supported by a technique we developed to obtain polygons with an increasing number of vertices starting from a unit square. The other follows a constraint programming approach and gives great control on the generated polygons. In particular, it may be used to find all n-vertex orthogonal polygons with no collinear edges that can be drawn in an \(\frac{n}{2} \times \frac{n}{2}\) grid, for small n, with symmetries broken.

Partitioning Orthogonal Polygons by Extension of All Edges Incident to Reflex Vertices: Lower and Upper Bounds on the Number of Pieces

Given an orthogonal polygon P, let |Π(P)| be the number of rectangles that result when we partition P by extending the edges incident to reflex vertices towards INT(P). In [4] we have shown that |Π(P)| ≤ 1+r+r 2, where r is the number of reflex vertices of P. We shall now give sharper bounds both for max p |Π(P)| and min p |Π(P)|. Moreover, we characterize the structure of orthogonal polygons in general position for which these new bounds are exact. We also present bounds on the area of grid n-ogons and characterize those having the largest and the smallest area.

2-Covered paths by a set of antennas with minimum power transmission range

In this paper we describe and solve the following geometric optimisation problem: given a set S of n points on the plane (antennas) and two points A and B, find the smallest radial range r@?@?^+ (power transmission range of the antennas) so that a path with endpoints A and B exists in which all points are within the range of at least two antennas. The solution to the problem has several applications (e.g., in the planning of safe routes). We present an O(nlogn) time solution, which is based on the second order Voronoi diagram. We also show how to obtain a path with such characteristics.

Estimating the Maximum Hidden Vertex Set in Polygons

It is known that the maximum hidden vertex set problem on a given simple polygon is NP-hard (Shermer, 1989), therefore we focused on the development of approximation algorithms to tackle it. We propose four strategies to solve this problem, the first two (based on greedy constructive search) are designed specifically to solve it, and the other two are based on the general metaheuristics simulated annealing and genetic algorithms. We conclude, through experimentation, that our best approximate algorithm is the one based on the Simulated Annealing metaheuristic. The solutions obtained with it are very satisfactory in the sense that they are always close to optimal (with an approximation ratio of 1.7, for arbitrary polygons; and with an approximation ratio of 1.5, for orthogonal polygons). We, also, conclude,that on average the maximum number of hidden vertices in a simple polygon (arbitrary or orthogonal) with n vertices is n/4.

Optimal 2-Coverage of a Polygonal Region in a Sensor Network

Wireless sensor networks are a relatively new area where technology is developing fast and are used to solve a great diversity of problems that range from museums’ security to wildlife protection. The geometric optimisation problem solved in this paper is aimed at minimising the sensors’ range so that every point on a polygonal region R is within the range of at least two sensors. Moreover, it is also shown how to minimise the sensors’ range to assure the existence of a path within R that stays as close to two sensors as possible.

Characterizing and covering some subclasses of orthogonal polygons

A grid n-ogon is a n-vertex orthogonal polygon that may be placed in a

Metaheuristic Approaches for the Minimum Vertex Guard Problem

\frac{n}{2}\times \frac{n}{2}