Professor Adjunto IVCentro de Informática · Universidade Federal de PernambucoRecife, Brazil
My research focuses on computational geometry, geometric probability and algorithms, with broader interests in discrete mathematics and theoretical computer science.
Current research
Recent preprints exploring the structure of discrete objects and the behavior of geometric algorithms.
An explicit geometric description of pattern-avoiding permutation polytopes connects lattice-point counting with real-rooted polynomials. Exact verification and an eventual theorem cover two dimension ranges; the intermediate range remains open.
Pedro M. M. de Castro
How much of the past should a geometric algorithm retain? This work analyzes an exponentially weighted state, comparing connection costs for random points with sharp adversarial bounds.
Pedro M. M. de Castro
Classifies all minimum blockers for nonnested perfect matchings and constructs ordered graphs exceeding a proposed extremal bound by a quadratic number of edges.
Studies optimal memory for edge-power costs in sequential Euclidean trees, including phase transitions and worst-case input sequences.
Studies the landmarks needed to identify edges after landmark names are removed from distance reports. Gives asymptotic bounds for fixed subdivision lengths and existence results for lengths two and three.
Shows that avoiding nested pairs requires more vertices to force a matching of one color. Explicit counterexamples cover every number of colors and target size at least three.
Random geometric structures, sequential connections and the trade-offs between memory and connection cost.
Exponential memory ↗Polytopes, lattice-point enumeration and the combinatorial structure behind Ehrhart polynomials.
Permutation polytopes ↗Delaunay triangulations, distribution-sensitive search and exact geometric computation.
Explore point-location strategies ↗From geometric ideas to reusable algorithms.
I have contributed to the Computational Geometry Algorithms Library (CGAL), with work on exact circular and spherical geometry, 3D triangulations, geometric sampling and sorting on the sphere.
Journal articles and conference work on geometric search, random structures, optimization and complexity.
Pedro Machado Manhães de Castro, Olivier Devillers
Discrete & Computational Geometry 60(1), pp. 200–219
Analyzes the expected length of Voronoi paths in high-dimensional Poisson-Delaunay triangulations and gives dimension-dependent bounds.
Daniel Binham, Pedro Machado Manhães de Castro, Antoine Vigneron
33rd International Symposium on Computational Geometry (SoCG 2017); Leibniz International Proceedings in Informatics (LIPIcs) 77, pp. 17:1–17:15
Studies reachability in planar subdivisions with directional constraints, with an efficient algorithm and a hardness result for a broader variant.
Pedro Machado Manhães de Castro, Quentin Mérigot, Boris Thibert
Numerische Mathematik 134(2), pp. 389–411
Uses intersections of confocal paraboloids and exact geometric computation to solve a far-field reflector problem numerically.
Pedro Machado Manhães de Castro, Olivier Devillers
Computer Aided Geometric Design 30(5), pp. 431–450
Develops practical distribution-sensitive point-location strategies that reuse previous queries, combining walking methods with a Delaunay hierarchy.
Sets, relations, logic, proof techniques, counting, recurrences, graphs and trees.
Linear systems, matrices, vector spaces, transformations, orthogonality, determinants and eigenvalues.
I am a faculty member at the Center for Informatics, Federal University of Pernambuco. My work includes Delaunay triangulations, geometric search, random structures and exact geometric computation.
Within discrete mathematics, I study connections between geometric and combinatorial structures, including graphs and their embeddings, polytopes and Ehrhart polynomials.
My computing education includes a Ph.D. at Université de Nice and INRIA (2010), a postdoctoral period at KAUST (2011), and B.Sc. and M.Sc. degrees at UFPE.
Since 2024, I have coordinated six editions of this extension course, strengthening mathematical foundations for a computing degree.
