P. Pérez-Lantero

activity

20112022

most citedOn balanced 4-holes in bichromatic point sets

9 citations · 22 across the 20 of their papers we have counts for

collaborators

27 papers

cs.CG2022★ 1 cited

Rectilinear Convex Hull of Points in 3D

Pablo Pérez-Lantero, Carlos Seara, Jorge Urrutia

Let $P$ be a set of $n$ points in $R^{3}$ in general position, and let $R C H (P)$ be the rectilinear convex hull of $P$ . In this paper we obtain an optimal $O (n lo g n)$ -time a…

cs.CG2019★ 2 cited

Maximum rectilinear convex subsets

Hernán González-Aguilar, David Orden, Pablo Pérez-Lantero +4

Let $P$ be a set of $n$ points in the plane. We consider a variation of the classical Erdős-Szekeres problem, presenting efficient algorithms with $O (n^{3})$ running time and $O(n^2)…

cs.CG2019

Matching points with disks with a common intersection

Clemens Huemer, Pablo Pérez-Lantero, Carlos Seara +1

We consider matchings with diametral disks between two sets of points R and B. More precisely, for each pair of matched points p in R and q in B, we consider the disk through p and…

cs.CG2018

Computing Coverage Kernels Under Restricted Settings

Jérémy Barbay, Pablo Pérez-Lantero, Javiel Rojas-Ledesma

We consider the Minimum Coverage Kernel problem: given a set $B$ of $d$ -dimensional boxes, find a subset of $B$ of minimum size covering the same region as $B$ . This problem is $\m…

math.CO2018

On the Diameter of Tree Associahedra

Jean Cardinal, Stefan Langerman, Pablo Pérez-Lantero

We consider a natural notion of search trees on graphs, which we show is ubiquitous in various areas of discrete mathematics and computer science. Search trees on graphs can be mod…

cs.CG2018

Colored ray configurations

Ruy Fabila-Monroy, Alfredo García, Ferran Hurtado +6

We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays a…

cs.CG2017★ 9 cited

On balanced 4-holes in bichromatic point sets

S. Bereg, J. M. Díaz-Báñez, R. Fabila-Monroy +5

Let $S = R \cup B$ be a point set in the plane in general position such that each of its elements is colored either red or blue, where $R$ and $B$ denote the points colored red and th…

math.CO2017★ 4 cited

$K_{1, 3}$ -covering red and blue points in the plane

Bernardo M. Ábrego, Silvia Fernández-Merchant, Mikio Kano +4

We say that a finite set of red and blue points in the plane in general position can be $K_{1, 3}$ -covered if the set can be partitioned into subsets of size $4$ , with $3$ points of…

cs.CG2017

Depth Distribution in High Dimensions

Jérémy Barbay, Pablo Pérez-Lantero, Javiel Rojas-Ledesma

Motivated by the analysis of range queries in databases, we introduce the computation of the Depth Distribution of a set $B$ of axis aligned boxes, whose computation gene…

cs.CG2016

Drawing the Almost Convex Set in an Integer Grid of Minimum Size

Frank Duque, Ruy Fabila-Monroy, Carlos Hidalgo-Toscano +1

In 2001, Károlyi, Pach and Tóth introduced a family of point sets to solve an Erdős-Szekeres type problem; which have been used to solve several other Edős-Szekeres type problems.…

cs.DS2016

Linear Separability in Spatial Databases

Gilberto Gutiérrez, Pablo Pérez-Lantero, Claudio Torres

Given two point sets $R$ and $B$ in the plane, with cardinalities $m$ and $n$ , respectively, and each set stored in a separate R-tree, we present an algorithm to decide whether $R$ …

cs.CG2015

Balanced Islands in Two Colored Point Sets in the Plane

Oswin Aichholzer, Nieves Atienza, Ruy Fabila-Monroy +5

Let $S$ be a set of $n$ points in general position in the plane, $r$ of which are red and $b$ of which are blue. In this paper we prove that there exist: for every $α\in \left [ 0,…

cs.DS2015

Adaptive Computation of the Klee's Measure in High Dimensions

Jérémy Barbay, Pablo Pérez-Lantero, Javiel Rojas-Ledesma

The KLEE'S MESURE of $n$ axis-parallel boxes in $R^{d}$ is the volume of their union. It can be computed in time within $O (n^{d /2})$ in the worst case. We describe three tec…

cs.DS2015

Refining the Analysis of Divide and Conquer: How and When

Jeremy Barbay, Carlos Ochoa, Pablo Perez-Lantero

Divide-and-conquer is a central paradigm for the design of algorithms, through which some fundamental computational problems, such as sorting arrays and computing convex hulls, are…

cs.DS2015

Adaptive Computation of the Swap-Insert Correction Distance

Jérémy Barbay, Pablo Pérez-Lantero

The Swap-Insert Correction distance from a string $S$ of length $n$ to another string $L$ of length $m \geq n$ on the alphabet $[1.. d]$ is the minimum number of insertions, and swap…

cs.DS2015

Interval Selection in the Streaming Model

Sergio Cabello, Pablo Pérez-Lantero

A set of intervals is independent when the intervals are pairwise disjoint. In the interval selection problem we are given a set $I$ of intervals and we want to find an in…

cs.CG2014

Area and Perimeter of the Convex Hull of Stochastic Points

Pablo Pérez-Lantero

Given a set $P$ of $n$ points in the plane, we study the computation of the probability distribution function of both the area and perimeter of the convex hull of a random subset $…

cs.CG2013

Independent and Hitting Sets of Rectangles Intersecting a Diagonal Line : Algorithms and Complexity

José R. Correa, Laurent Feuilloley, Pablo Pérez-Lantero +1

Finding a maximum independent set (MIS) of a given fam- ily of axis-parallel rectangles is a basic problem in computational geom- etry and combinatorics. This problem has attracted…

cs.CG2013★ 2 cited

Matching colored points with rectangles

L. E. Caraballo, C. Ochoa, P. Pérez-Lantero +1

Let $S$ be a point set in the plane such that each of its elements is colored either red or blue. A matching of $S$ with rectangles is any set of pairwise-disjoint axis-aligned rec…

cs.CG2013★ 2 cited

Drawing the double circle on a grid of minimum size

Sergey Bereg, Ruy Fabila-Monroy, David Flores-Peñaloza +2

In 1926, Jarník introduced the problem of drawing a convex $n$ -gon with vertices having integer coordinates. He constructed such a drawing in the grid $[1, c \cdot n^{3/2}]^{2}$ for so…

math.CO2012

New results on the coarseness of bicolored point sets

J. M. Díaz-Báñez, R. Fabila-Monroy, P. Pérez-Lantero +1

Let $S$ be a 2-colored (red and blue) set of $n$ points in the plane. A subset $I$ of $S$ is an island if there exits a convex set $C$ such that $I = C \cap S$ . The discrepancy of an…

cs.CC2012

New results on stabbing segments with a polygon

José Miguel Díaz-Báñez, Matias Korman, Pablo Pérez-Lantero +3

We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon $P$ if at least one of its two endpoint…

cs.CG2012

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…

cs.CG2012

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…

Rectilinear Convex Hull of Points in 3D

Maximum rectilinear convex subsets

Matching points with disks with a common intersection

Computing Coverage Kernels Under Restricted Settings

On the Diameter of Tree Associahedra

Colored ray configurations

On balanced 4-holes in bichromatic point sets

K1,3​-covering red and blue points in the plane

Depth Distribution in High Dimensions

Drawing the Almost Convex Set in an Integer Grid of Minimum Size

Linear Separability in Spatial Databases

Balanced Islands in Two Colored Point Sets in the Plane

Adaptive Computation of the Klee's Measure in High Dimensions

Refining the Analysis of Divide and Conquer: How and When

Adaptive Computation of the Swap-Insert Correction Distance

Interval Selection in the Streaming Model

Area and Perimeter of the Convex Hull of Stochastic Points

Independent and Hitting Sets of Rectangles Intersecting a Diagonal Line : Algorithms and Complexity

Matching colored points with rectangles

Drawing the double circle on a grid of minimum size

New results on the coarseness of bicolored point sets

New results on stabbing segments with a polygon

The 1-Center and 1-Highway problem

Locating a single facility and a high-speed line

$K_{1, 3}$ -covering red and blue points in the plane