10 citations · 31 across the 27 of their papers we have counts for
14 papers · 1 filter
Optimizing Line Segment Inspection with Limited-Range Drones
José-Miguel Díaz-Báñez, José-Manuel Higes, Alina Kasiuk +1
Optimization problems with drones are widely studied in a variety of civilian tasks, mainly due to their ability to traverse rough terrains and to carry cameras and other sensors f…
Filming runners with drones is hard
José-Miguel Díaz-Báñez, Ruy Fabila-Monroy
The use of drones or Unmanned Aerial Vehicles (UAVs) for aerial photography and cinematography is becoming widespread. The following optimization problem has been recently consider…
Mathematics and Flamenco: An Unexpected Partnership
José-Miguel Díaz-Báñez
In this paper, we present a series of mathematical problems which throw interesting lights on flamenco music. More specifically, these are problems in discrete and computational ma…
Optimal Placement of Base Stations in Border Surveillance using Limited Capacity Drones
S. Bereg, J. M. Díaz-Báñez, M. Haghpanah +8
Imagine an island modeled as a simple polygon with vertices whose coastline we wish to monitor. We consider the problem of building the minimum number of refueling stations…
On Optimal Coverage of a Tree with Multiple Robots
I. Aldana-Galván, J. C. Catana-Salazar, J. M. Díaz-Báñez +5
We study the algorithmic problem of optimally covering a tree with mobile robots. The tree is known to all robots, and our goal is to assign a walk to each robot in such a way…
A Note on Empty Balanced Tetrahedra in Two colored Point sets in
José M. Díaz-Bañez, Ruy Fabila-Monroy, Jorge Urrutia
Let be a set of red and blue points in general position in . Let be a tetrahedra with vertices on . We say that is \emph{empty} if it does not…
On the Number of Order Types in Integer Grids of Small Size
Luis E. Caraballo, José-Miguel Díaz-Báñez, Ruy Fabila-Monroy +3
Let and be two sets of labeled points in general position in the plane. We say that these two point sets have the same order type if for…
A Polynomial Algorithm for Balanced Clustering via Graph Partitioning
Luis-Evaristo Caraballo, José-Miguel Díaz-Báñez, Nadine Kroher
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the c…
On balanced 4-holes in bichromatic point sets
S. Bereg, J. M. Díaz-Báñez, R. Fabila-Monroy +5
Let be a point set in the plane in general position such that each of its elements is colored either red or blue, where and denote the points colored red and th…
Balanced Islands in Two Colored Point Sets in the Plane
Oswin Aichholzer, Nieves Atienza, Ruy Fabila-Monroy +5
Let be a set of points in general position in the plane, of which are red and of which are blue. In this paper we prove that there exist: for every $α\in \left [ 0,…
The 1-Center and 1-Highway problem
José Miguel Díaz-Báñez, Matias Korman, Pablo Pérez-Lantero +1
We study a variation of the 1-center problem in which, in addition to a single supply facility, we are allowed to locate a highway. This highway increases the transportation speed…
Locating a single facility and a high-speed line
José Miguel Díaz-Báñez, Matias Korman, Pablo Pérez-Lantero +1
In this paper we study a facility location problem in the plane in which a single point (facility) and a rapid transit line (highway) are simultaneously located in order to minimiz…
On the number of radial orderings of planar point sets
José M. Díaz-Bañez, Ruy Fabila-Monroy, Pablo Pérez-Lantero
Given a set of points in the plane, a \emph{radial ordering} of with respect to a point (not in ) is a clockwise circular ordering of the elements in by angl…
Locating a service facility and a rapid transit line
J. M. Díaz-Bañez, M. Korman, P. Pérez-Lantero +1
In this paper we study a facility location problem in the plane in which a single point (facility) and a rapid transit line (highway) are simultaneously located in order to minimiz…