Computational geometry, geometric probability, algorithms and discrete mathematics. Preprints are identified separately from journal and conference publications.
arXiv, preprint, v1
Describes the geometry of pattern-avoiding permutation polytopes and proves real-rootedness in two dimension ranges. The intermediate range remains open.
Discrete mathematics
arXiv, preprint, v2
Analyzes connection costs for sequential points using an exponentially weighted moving state, comparing random-input performance with adversarial robustness.
Geometric probability
arXiv, preprint, v2 · 8 October 2026 · 30 pages, 11 figures, 1 algorithm
Classifies all minimum blockers for nonnested perfect matchings and constructs ordered graphs exceeding a proposed extremal bound by a quadratic number of edges.
Discrete mathematics
arXiv, preprint, v2
Studies optimal memory for edge-power costs in sequential Euclidean trees, including phase transitions and worst-case input sequences.
Geometric probability
Zenodo, preprint, v3.0
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.
Discrete mathematics
Hexagon, preprint, v1 · 18 October 2026
Constructs explicit counterexamples to the conjecture of Barát, Gyárfás and Tóth with equally sized targets, for every number of colors and target size at least three. These examples show that excluding nested pairs raises the classical matching Ramsey threshold by at least one vertex.
Discrete mathematics
Proceedings of the 31st Canadian Conference on Computational Geometry (CCCG 2019), pp. 99–104
Establishes lower bounds for converting Voronoi-related diagrams and gives a randomized incremental construction for an Apollonius diagram.
Computational geometry
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.
Geometric probability
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.
Computational geometry
Numerische Mathematik 134(2), pp. 389–411
Uses intersections of confocal paraboloids and exact geometric computation to solve a far-field reflector problem numerically.
Computational geometry
Proceedings of the thirtieth annual symposium on Computational geometry, pp. 308–317
Studies the combinatorics and computation of paraboloid and ellipsoid intersections, with an application to reflector design.
Computational geometry
Computers & Graphics 38, pp. 399–409
Studies invariances associated with single-curved manifolds and applies the resulting geometric framework to mesh segmentation.
Geometry and graphics
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.
Computational geometry
2012 25th SIBGRAPI Conference on Graphics, Patterns and Images, pp. 158–165
Develops an invariance framework for single-curved manifolds related to illumination and developable-surface geometry.
Geometry and graphics
Proceedings of the twenty-seventh annual symposium on Computational geometry, pp. 295–296
A JavaScript pedagogical demonstration of point-location strategies, originally designed for desktop computers.
Computational geometry
Operations Research Letters 39(1), pp. 44–48
Analyzes worst-case and expected edge-power costs of Euclidean insertion trees and stars.
Geometric probability
2011 Proceedings of the Thirteenth Workshop on Algorithm Engineering and Experiments (ALENEX), pp. 127–138
Introduces distribution-sensitive triangulation searches that exploit previous queries through Keep, Jump, & Walk and related strategies.
Computational geometry
Experimental Algorithms (SEA 2010); Lecture Notes in Computer Science 6049, pp. 462–473
Presents robust incremental methods for Delaunay triangulations of points on or close to a sphere, implemented with CGAL.
Computational geometry
Computational Geometry 42(6-7), pp. 536–550
Presents a robust spherical-geometry kernel and evaluates exact arrangements of circles on a sphere.
Computational geometry
Abstracts of the 25th European Workshop on Computational Geometry, pp. 231–234
Conference abstract on efficiently updating Delaunay triangulations for converging point-relocation sequences.
Computational geometry
Computer Graphics Forum 28(5), pp. 1465–1474
Uses vertex-tolerance filters to accelerate Delaunay updates when points move by small amounts.
Computational geometry
Abstracts of the 23rd European Workshop on Computational Geometry, pp. 219–222
Investigates efficient exact computations for circles and circular arcs in CGAL, with VLSI data used for evaluation.
Computational geometry
II Workshop de Jogos e Entretenimento Digital, pp. 33–40
Early conference work on using idleness and distance in heuristic agents for a patrolling task; the website provides citation metadata only.
Algorithms
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