CARABALLO DE LA CRUZ , Luis Evaristo

Las matemáticas siempre han sido una pieza fundamental en el desarrollo de la robótica, así como los problemas de robótica han jugado un importante papel en el desarrollo de las matemáticas. Esta tesis está motivada por el creciente interés en problemas que aparecen en aplicaciones de robótica aérea, específicamente, está enfocada en sistemas...

Given a finite set of weighted points in Rd (where there can be negative weights), the maximum box problem asks for an axis-aligned rectangle (i.e., box) such that the sum of the weights of the points that it contains is maximized. We consider that each point of the input has a probability of being present in the final random point set, and...

Melodic similarity measurement is of key importance in Music Information Retrieval. In this paper, we use geometric matching techniques to measure the similarity between two monophonic melodies. We propose efficient algorithms for optimization problems inspired in two operations on melodies: scaling and compressing. In the scaling problem, an...

Let and be two sets of n labeled points in general position in the plane. We say that these two point sets have the same order type if for every triple of indices , is above the directed line from to if and only if is above the directed line from to . In this paper we give the first non-trivial lower bounds on the number of different...

In the minimum-weight many-to-many point matching problem, we are given a set R of red points and a set B of blue points in the plane, of total size N, and we want to pair up each point in R to one or more points in B and vice versa so that the sum of distances between the paired points is minimized. This problem can be solved in O(N3) time by...