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In the Nearest Neighbor problem (NN), the objects in the database that are nearer to a given query object than any other objects in the database have to be found. In the conceptually inverse problem, Reverse Nearest Neighbor problem (RNN), objects that have the query object as their nearest neighbor have to be found. Reverse Nearest Neighbors queries have… (More)

Let S be a point set in the plane in general position, such that its elements are partitioned into k classes or colors. In this paper we study several variants on problems related to the Erdős-Szekeres theorem about subsets of S in convex position, when additional chromatic constraints are considered. ∗Most of this work was made possible by the Picasso… (More)

- M. Carmen Hernando, Mercè Mora, Ignacio M. Pelayo, Carlos Seara, David R. Wood
- Electronic Notes in Discrete Mathematics
- 2007

A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let Gβ,D be the set of graphs with metric dimension β and diameter D. It is well-known that the minimum order of a graph in Gβ,D is exactly β +… (More)

- José Cáceres, M. Carmen Hernando, +4 authors David R. Wood
- SIAM J. Discrete Math.
- 2007

A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. This paper studies the metric dimension of cartesian products G H. We prove that the metric dimension of G G is tied in a strong sense to the minimum… (More)

- Boris Aronov, Franz Aurenhammer, +4 authors Carlos Seara
- CCCG
- 2005

Given a set P of points in the plane, a set of points Q is a weak ε-net with respect to a family of sets S (e.g., rectangles, disks, or convex sets) if every set of S containing ε|P | points contains a point of Q. In this paper, we determine bounds on εi , the Preprint submitted to Elsevier Science 10 February 2008 smallest epsilon that can be guaranteed… (More)

- M. Carmen Hernando, Tao Jiang, Mercè Mora, Ignacio M. Pelayo, Carlos Seara
- Discrete Mathematics
- 2005

Given a graph G and a subset W ⊆ V (G), a Steiner W -tree is a tree of minimum order that contains all of W . Let S(W ) denote the set of all vertices in G that lie on some Steiner W -tree; we call S(W ) the Steiner interval of W . If S(W ) = V (G), then we call W a Steiner set of G. The minimum order of a Steiner set of G is called the Steiner number of G.… (More)

- José Cáceres, M. Carmen Hernando, Mercè Mora, Ignacio M. Pelayo, María Luz Puertas, Carlos Seara
- Discrete Applied Mathematics
- 2008

A vertex v is a boundary vertex of a connected graph G if there exists a vertex u such that no neighbor of v is further away from u than v. Moreover, if no vertex in the whole graph V (G) is further away from u than v, then v is called an eccentric vertex of G. A vertex v belongs to the contour of G if no neighbor of v has an eccentricity greater than the… (More)

- Sergey Bereg, Sergio Cabello, José Miguel Díaz-Báñez, Pablo Pérez-Lantero, Carlos Seara, Inmaculada Ventura
- Comput. Geom.
- 2012

In this paper we study the following problem: Given sets R and B of r red and b blue points respectively in the plane, find a minimum-cardinality set H of axis-aligned rectangles (boxes) so that every point in B is covered by at least one rectangle of H, and no rectangle of H contains a point of R. We prove the NP-hardness of the stated problem, and give… (More)

- Sergey Bereg, José Miguel Díaz-Báñez, Carlos Seara, Inmaculada Ventura
- Comput. Geom.
- 2007

An α-siphon of width w is the locus of points in the plane that are at the same distance w from a 1-corner polygonal chain C such that α is the interior angle of C. Given a set P of n points in the plane and a fixed angle α, we want to compute the widest empty α-siphon that splits P into two non-empty sets. We present an efficient O(n log n)-time algorithm… (More)

- José Cáceres, M. Carmen Hernando, Mercè Mora, Ignacio M. Pelayo, María Luz Puertas, Carlos Seara
- Discrete Mathematics
- 2006

Let G be a finite simple connected graph. A vertex v is a boundary vertex of G if there exists a vertex u such that no neighbor of v is further away from u than v. We obtain a number of properties involving different types of boundary vertices: peripheral, contour and eccentric vertices. Before showing that one of the main results in [3] does not hold for… (More)