VENTURA MOLINA , Inmaculada

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An α-siphon is the locus of points in the plane that are at the same distance ǫ from a polygonal chain consisting of two half-lines emanating from a common point such that α is the interior angle of the half-lines. Given a set S of n points in the plane and a fixed angle α, we want to compute an α-siphon of largest width ǫ such that no points...

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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 log3...

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...

We study the problem of fitting a two-joint orthogonal polygonal chain to a set S of n points in the plane, where the objective function is to minimize the maximum orthogonal distance from S to the chain. We show that this problem can be solved in Θ(n) time if the orientation of the chain is fixed, and in Θ(n logn) time when the orientation is...

We study the following problem: Given a set of red points and a set of blue points on the plane, find two unit disks CR and CB with disjoint interiors such that the number of red points covered by CR plus the number of blue points covered by CB is maximized. We give an algorithm to solve this problem in O(n8/3 log2 n) time, where n denotes the...

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...

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 S be a set of n points on the plane in general position such that its elements are colored red or blue. We study the following problem: Find a largest subset of S which can be enclosed by the union of two, not necessarily disjoint, axis-aligned rectangles R and B such that R (resp. B) contains only red (resp. blue) points. We prove that...