Fine-Grained Complexity Theory: Conditional Lower Bounds for Computational Geometry

@article{Bringmann2021FineGrainedCT,
  title={Fine-Grained Complexity Theory: Conditional Lower Bounds for Computational Geometry},
  author={Karl Bringmann},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.10283}
}
Fine-grained complexity theory is the area of theoretical computer science that proves conditional lower bounds based on the Strong Exponential Time Hypothesis and similar conjectures. This area has been thriving in the last decade, leading to conditionally best-possible algorithms for a wide variety of problems on graphs, strings, numbers etc. This article is an introduction to fine-grained lower bounds in computational geometry, with a focus on lower bounds for polynomial-time problems based… 
1 Citations
Conditional Lower Bounds for Dynamic Geometric Measure Problems
TLDR
New polynomial lower bounds are given for a number of dynamic measure problems in computational geometry, including those for counting maximal or extremal points in R3, different variants of Klee’s Measure Problem, and problems related to finding the largest empty disk in a set of points.

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