Theory & Algorithms · Computer Science & AI
Computational Geometry
The newest papers in Computational Geometry that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
90 papers, from 7 September 2026 to 4 November 2026: 90 arXiv preprints.
Get the few papers worth your time in Computational Geometry every morning.
Follow Computational Geometry and ReadSearch reads its new papers each day, then brings you the few worth reading, each with its key finding in a sentence.
Newest papers
Does RRT* Work on Uneven Terrain Meshes?
The optimal rapidly exploring random tree (RRT*) is proven asymptotically optimal on open subsets of Euclidean space with straight-line local planning.Softmax Attention with Any Temperature in Fixed Dimension: Matching the Best Known Maximum-Inner-Product Bounds
Attention is central to modern AI models for language, vision, and scientific modeling.Constant-Round Massively Parallel Algorithms for Approximate MSTs in Metric Spaces
We develop a unified algorithmic framework for computing approximate minimum spanning trees (MSTs) in metric spaces in the fully scalable Massively Parallel Computation (MPC) model.Resolving Tusnády's Problem
We prove a lower bound of $Ω_d((\log N)^{d-1/2})$ for the worst-case combinatorial discrepancy of $N$-point sets with respect to anchored boxes in every fixed dimension $d\ge3$.Stacking Stars: Minimum-Area Packing with and without Rotation
We study the problem of packing a given set of polygons into a minimum-area convex container, that is, placing them without overlap so as to minimize the area of their convex hull.Binary Huffman Coding with Unequal Letter Costs Is NP-Complete
Binary prefix coding assigns prefix-free binary words to symbols to minimize their frequency-weighted cost.Geometric Bin Packing Beyond Convexity: Approximation Schemes without Augmentation
We study the geometric bin packing problem for simple polygonal regions, i.e., non-degenerate, connected, rational regions, in the minimum number of unit-square bins, allowing only translations.Faster Planar Diameter using Pseudoline Envelopes
We give an improved algorithm for weighted directed planar diameter that runs in $\widetilde{O}(n^{3/2})$ time.Pair-Relative Partial Equivariance for Rotation-Robust Keypoint Descriptor Matching
Learned keypoint descriptors trained on upright imagery often fail under large in-plane rotation.An $\mathsf{FPRAS}$ for Mixed Volumes
We design the first fully polynomial-time randomized approximation scheme ($\mathsf{FPRAS}$) to estimate the mixed volume of $n$ arbitrary compact convex sets in $\mathbb{R}^{n}$ specified by weak…Graphs Have Structure: Declarative Manifolds, 3D Z-Order Monoid Roll-ups, and Zero-Simulation Visual Analytics in a Graph DBMS
Every real-world graph is embedded in an ambient structural manifold: proteins fold in Euclidean space ($R^3$), telecom networks sit on a planetary surface ($S^2 \times R$), and ontologies and…Representation-Aware Closed-Surface Parameterization: Exact Sensitivity Analysis and Pole-Aware Planar Preconditioning
Surface parameterization is a fundamental task in geometry processing and shape analysis.CuPH: Parallel Cubical Persistent Homology via Level-Synchronous Component Tracking
Persistent homology (PH) is a mathematically principled multi-scale topological descriptor of shape and connectivity in data.Optimal Average Distortion for Non-Expansive Embeddings of Euclidean Metrics into the Line: With applications to cut-matching games and vertex expansion
We show that any $n$-point Euclidean metric admits a non-expansive embedding into the line with average distortion at most $O\left(\sqrt{\frac{\log n}{\log\log n}}\right)$, matching a known lower…Implicit Additively Weighted Geodesic Voronoi Diagrams and Applications
Let $P$ be a simple polygon with $m$ vertices.Catenary Visibility: A Geometric Framework for Planning with Tethered Robots
This paper introduces \emph{catenary visibility}, a new geometric visibility concept for a robotic system consisting of a ground robot tethered to an aerial drone.PhysicsNeMo-Mesh: GPU-Native Meshes and Simulation Cases for Physics AI
PhysicsNeMo-Mesh is the mesh module of the open-source PhysicsNeMo library.Four-Coloring Planar Graphs in Linear Time
The famous Four Color Theorem (4CT) states that any planar graph can be colored with four colors, but how do we find a 4-coloring?Compressed Orientation Reachability Maps for Sub-Second Robotic Needle Entry Point Planning
In the context of multi-stage trajectory planning for robotic percutaneous liver interventions, identifying a kinematically feasible entry point remains a critical computational bottleneck.Constant-Factor Approximation for Capacitated Clustering in Low Dimension with $(1+ε)k$ Centers
In many applications of $k$-median and $k$-means, including load balancing and redistricting, each center can serve only a bounded number of clients.