Product Information
Description
An annual survey of the cs.CG arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 108 papers and organised into 40 chapters, it maps the year by the field's research sub-directions.
Book framework (share of the year's output):
- Euclidean Minimum Spanning Trees and Metric Approximation (21.5%) — This subfield investigates the structural properties, complexity bounds, and approximation algorithms for Euclidean Minimum Spanning Trees and related metric space problems.
- Voronoi Diagrams and Topological Persistence Optimization (19.2%) — Research focuses on integrating Voronoi-based geometric structures with topological persistence diagrams for optimization and learning applications.
- Computational Complexity of Geometric Search and Embedding (14.2%) — This area addresses algorithmic hardness and efficient computation for high-dimensional point set problems, curve computation, and geometric embeddings.
- Intersection Graphs and Planar Graph Drawing (11.8%) — Studies cover the representation, drawing, and algorithmic properties of planar graphs, disk intersection graphs, and string graphs.
- Topological Data Analysis and Graph Learning (8.4%) — This subfield applies topological signatures and graph-based methods to data analysis, trajectory imputation, and interpretable machine learning.
- Dynamic Convex Hulls and Polyhedral Geometry (7.2%) — Focuses on algorithms for computing, reconstructing, and maintaining convex hulls and polyhedral structures under dynamic or partial information constraints.
- Geometric Spanners and Implicit Representations (6.9%) — Investigates sparse geometric representations, spanners, and implicit data structures for efficient geometric computation in various metrics.
- Geometric Design and Hilbert Geometry Applications (6.9%) — Explores computational geometry techniques for 3D design, lattice structures, and Hilbert geometry, with applications in computer vision and modeling.
- Persistent Homology Algorithms and Stability (4.0%) — This niche area develops efficient algorithms for computing persistent homology and analyzes its stability in high-dimensional topological data analysis.
Each sub-direction is covered across three chapters — how it framed its questions, the strength of its key findings, and its open debates and frontiers — so the reader gets a traceable picture of what this part of the field actually produced over the year.
