Ongoing and Past Projects

Lifelong Project

Genesis 1:28 In close collaboration with Ketty A. de Rezende, since 1979.
Environment for development of human beings and animation of human nature.

Projects involving Graduate Supervisions

Doctoral Dissertations (Ph.D.)

From Consensus to Curriculum: Advancing Deep Semi-Supervised Learning via Meta-Pseudo-Labeling on 2D Projections David Aparco-Cardenas, 2026 [Advisor]
Investigation into deep semi-supervised learning that replaces large validation sets with graph-based pseudo-labeling on 2D embeddings. Combines consensus, co-training, contrastive and active learning, and curriculum strategies to train custom CNNs from scratch.
Exact Algorithms and Heuristics for Optimization Problems on the Spread of Information on Social Networks Felipe de Carvalho Pereira, 2024 [Advisor]
Investigation of combinatorial optimization and row-generation algorithms for information propagation and the Perfect Awareness problem in social graphs.
Exact and Heuristic Solutions for Optimal Polygon Construction Problems Natanael Ramos, 2023 [Co-advisor]
Research on optimization methods for constructing geometric figures, focusing on maximizing or minimizing area and perimeter under constraints.
Geometric Decomposition Problems Allan Sapucaia Barboza, 2022 [Advisor]
Algorithmic study on the partitioning of complex geometric shapes into simpler convex components or minimal subdivisions.
Exact Solutions for the Geometric Firefighter Problem and Variants Maurício José de Oliveira Zambon, 2018 [Advisor]
Applying integer linear programming to solve fire containment and spreading problems within geometric and graph-based frameworks.
Visual Analytics Applied to Image Analysis Paulo Eduardo Rauber, 2017 [Co-advisor]
Development of interactive visual analytics tools to interpret deep learning models and high-dimensional projections of image datasets.
Combinatorial Optimization Problems in Cartographic Data Visualization Rafael Ghussn Cano, 2016 [Co-advisor]
Design of algorithms for label placement and symbol displacement in maps, balancing aesthetic clarity with geometric precision.
Machine Learning with Real-Time Data Annotation Priscila Tiemi Maeda Saito, 2014 [Co-advisor]
Integrating active learning and human feedback loops into machine learning pipelines to optimize real-time data classification.
Computational Geometry in Spaces with Non-Euclidean Metrics Mário Massato Harada, 2000 [Advisor]
Study of fundamental geometric algorithms and proximity structures under non-standard distance metrics and their applications.

Master's Theses (M.Sc.)

Iterative Optimum-Path Forest: a Graph-Based Data Clustering Framework David Aparco-Cardenas, 2021 [Advisor]
Developing a graph-based framework for clustering using path optimization and connectivity criteria in complex feature spaces.
Exact and Heuristic Algorithms for the Perfect Awareness Problem Felipe de Carvalho Pereira, 2021 [Advisor]
Exploring social network influence models to find minimum seed sets that guarantee total information spread across a graph.
Metaheuristics Applied to the Selective Firefighter Problem in Graphs Alan Martins Silva, 2019 [Co-advisor]
Implementation of metaheuristic strategies to optimize resource allocation in graph-based containment scenarios.
A Computational Study of the Firefighter Problem in Graphs Natanael Ramos, 2018 [Co-advisor]
Theoretical and experimental analysis of graph-based firefighting strategies and their inherent computational difficulty.
Algorithms for Disk Coverage of Segments Anderson Toshiyuki Sasaki, 2014 [Advisor]
Geometric algorithms for the set cover variant where a set of line segments must be covered by a minimum number of disks.
Solving the Art Gallery Problem: A Practical and Robust Method for Optimal Point Guard Positioning Davi Colli Tozoni, 2014 [Co-advisor]
A robust implementation for the Art Gallery Problem using iterative visibility discretization and exact mathematical solvers.
Exact Solutions for the Art Gallery Chromatic Problem Maurício José de Oliveira Zambon, 2014 [Advisor]
Optimization of guard placement with chromatic constraints to ensure minimum observers in complex polygonal domains.
An Efficient Algorithm for the Natural Antenna Positioning Problem Bruno Espinosa Crepaldi, 2014 [Co-advisor]
Optimizing sensor and antenna placement in varied terrains using visibility analysis and efficient geometric coverage.
Exact Algorithms for Minimum Dilation Problems in Geometric Graphs Aléx Fernando Brandt, 2014 [Co-advisor]
Computational study of network design focusing on spanners and dilation minimization in geometric environments.
Visibility Graph Problems André Carvalho Silva, 2013 [Advisor]
Study of the combinatorial properties and characterization of graphs representing mutual visibility within simple polygons.
New Learning Algorithms for Pattern Classification Using Optimum-Path Forest César Christian Castelo-Fernández, 2011 [Advisor]
Analysis of supervised learning strategies within the OPF framework to improve overall pattern recognition accuracy.
Proportional Symbol Maps Guilherme Kunigami, 2011 [Advisor]
Developing algorithms for the automated placement and conflict resolution of proportional symbols in cartography.
An Exact Algorithm for an Art Gallery Problem Marcelo Castilho Couto, 2010 [Co-advisor]
Exact methods using integer programming to solve visibility-based guarding problems in orthogonal and simple polygons.
Geometric Problems in GF Geometry Fábio Dalla Costa Figueiredo, 2005 [Advisor]
Exploration of geometric algorithms and data structures defined over finite fields (Galois Fields).
A Visualizer for the Oriented Projective Plane using CGAL Fábio Pakk Selmi-Dei, 2005 [Advisor]
Development of a software tool for visualizing robust geometric primitives within the oriented projective plane using CGAL.
Implementation of the Oriented Projective Plane in CGAL Alessandra Guaracy de Oliveira, 2004 [Advisor]
Technical implementation of robust data structures for oriented projective geometry to enhance CGAL's library.
Order-k Voronoi Diagrams in Oriented Projective Geometry Rodrigo Bittencourt Westrupp, 1999 [Advisor]
Algorithmic development of higher-order proximity subdivisions within projective geometric environments.
Voronoi Diagram Generalizations via Conics in the Oriented Projective Plane Guilherme Albuquerque Pinto, 1998 [Advisor]
Exploration of generalized Voronoi structures for conic-based distance metrics in projective space.
Proximity and Shortest Path Problems on Polyhedral Surfaces Gutemberg Bezerra Guerra Filho, 1998 [Advisor]
Efficient algorithms for computing geodesic distances and shortest paths on 3D polyhedral meshes.
Exact Computation in Oriented Projective Geometry and Degeneracy Treatment César Nivaldo Gon, 1996 [Advisor]
Robust kernels for managing numerical precision and degenerate cases in oriented projective geometric calculations.
Point Pattern Matching with Perturbation Eduardo Aguiar Patrocínio, 1996 [Advisor]
Identification of patterns in point sets subject to perturbation, noise, and geometric transformations.
Search Techniques and Structures in Multidimensional Spaces Renato Fileto, 1994 [Advisor]
Comparative study of spatial indexing structures to support efficient multidimensional data queries.
GeoLab: An Environment for Development of Algorithms in Computational Geometry Welson Régis Jacometti, 1992 [Advisor]
Creation of an integrated software laboratory for prototyping, testing, and dynamic visualization of geometric algorithms.

Projects involving Undergraduate Supervisions (Scientific Initiation)

Graph Burning Problem with Propagation Radius r Lucas Souza Guimarães, 2025 [Advisor]
Exact IP-based results for the graph burning problem generalized to radius r on paths/cycles, and upper bounds for broader families, including heuristic approaches for efficiently computing the r-burning number.
Heuristics for Determining Inversion Distance between Triangulations Yuri Corrêa Pinto Soares, 2016 [Advisor]
Heuristic approaches for computing the transformation distance between distinct triangulations of the same point set.
Mathematical Models for Rectangle Escape Problems Allan Sapucaia Barboza, 2016 [Advisor]
Modeling and solving optimization problems related to moving rectangles out of constrained polygonal regions.
Optimization of Virtual Machine Allocation for Cloud Computing Matheus de Souza Ataíde, 2016 [Advisor]
Analysis of bin-packing variants to optimize resource management and machine allocation in cloud environments.
Weighted Point Partition Problems on Quadrilateral Grids Mateus Augusto Bellomo Agrello Ruivo, 2016 [Advisor]
Geometric algorithms for partitioning weighted point sets within structured quadrilateral grids.
Visualizing Planar Subdivisions: Quad-Edge Structures Flávio Ivan da Silva, 2006 [Advisor]
Software development for the interactive visualization of topological Quad-Edge data structures.
Visualizing Planar Subdivisions: Half-Edge Structures Flávio Ivan da Silva, 2005 [Advisor]
Implementation of visualization tools for the Half-Edge data structure in computational geometry.
A Framework for Programming Algorithm Animations Fábio Pakk Selmi-Dei, 2002 [Advisor]
Development of a software framework to simplify the creation of educational animations for complex algorithms.
Planar Visualizer for Oriented Projective Geometry Alexandre Volpim, 1998 [Advisor]
Interactive tool for rendering and manipulating geometric primitives in the oriented projective plane.
Data Structure and Algorithm Animations on Macintosh Felipe Carneiro Calheiros, 1996 [Advisor]
Early work on graphical animation of fundamental data structures and algorithms on the Macintosh platform.
GUI for Oriented Projective Geometry Computing Environment Ilídio J. Antunes, 1995 [Advisor]
User interface design for a specialized software laboratory focused on oriented projective geometry.
Astral: Algorithm and Data Structure Animation System Islene Calciolari Garcia, 1995 [Advisor]
The "Astral" system development for high-quality, flexible algorithm and data structure visualization.
Visualization Techniques for Algorithms Luciana Barbieri, 1995 [Advisor]
Research on visual methodologies to represent and animate complex data structures dynamically.
Implementation and Animation of Geometric Algorithms Rodrigo T. Ferreira, 1994 [Advisor]
Software implementation of geometric algorithms with integrated step-by-step graphical animation.
Animation and Dynamization of Data Structures Eduardo Aguiar Patrocínio, 1993 [Advisor]
Exploring dynamic updates and visual representation of evolving geometric data sets in real-time.
Geometric Algorithms, Dynamization, and Decomposability César Nivaldo Gon, 1993 [Advisor]
Study of decomposable geometric problems and their behavior in dynamic, changing environments.
Dynamization of Data Structures Laerte Ferreira Morgado, 1993 [Advisor]
Focused on data structures that support efficient updates while maintaining critical geometric properties.
Algorithm Animation Framework Eduardo Aguiar Patrocínio, 1992 [Advisor]
Early development of visualization modules for algorithm performance analysis and academic teaching.

Older Research Projects

Smallest Dilation Circa 2013
Algorithms for computing the smallest dilation substructure of a given topological metric structure.
Chromatic Art Gallery Circa 2012
Exact algorithms for minimizing the number of colors required to guide a robot within a polygonal environment.
Interactive Image Segmentation Circa 2012
Semi-supervised image segmentation and object identification.
Covering Geometric Objects with Disks Circa 2011
Approximation algorithms to minimize the total cost for covering given geometric objects with disks under a polynomial cost function on the disks' radii.
Active Learning Paradigms for Pattern Recognition Circa 2011
Semi-supervised image annotation that rely on a priori data reduction and organization.
Characterization of Visibility Graphs of Fans 2011-2013
Studying properties of visibility graphs of (pseudo-)fans.
Supervised Pattern Recognition Images Circa 2010
Effective and efficient algorithms for pattern recognition in the context of (semi-)supervised machine learning.
Exact Algorithms for Hard Problems in Symbol Maps Visualization Circa 2008
Exact algorithms for solving hard problems on map visualization.
Art Gallery Circa 2006
Exact algorithms for determining the smallest number of cameras that can guard a polygonal art gallery.
SubdiViewer (2004-2007):
Visualization tool for data structures representing planar subdivisions (Linux and Windows).
Geometry of curves (2004-2006):
Investigation of non-Euclidian geometries based on families of curves along with the development of a geometric tool (GFViewer) for creating and manipulating objects in said geometries.
T2 in CGAL and T2Viewer (2002-2007):
Extension of CGAL to the oriented projective plane T2 along with a Dynamic Visualization System (Linux).
Astral (1997-2003):
Environment for animation of algorithms and data structures (MacOS and Windows).
GeoPrO (1994-1999):
Distributed programming environment and visualization system for the oriented projective plane (Irix).
EGOLib (1991-1996):
Elementary Graphics Objects Library built over XLib and XView (SunOS).
AnimA (1991-1996):
Environment for animation of algorithms and data structures (SunOS).
GeoLab (1990-1993):
Environment for development and animation of geometric algorithms (SunOS).