An adaptive quadtree algorithm with curvature-guided Monte Carlo sampling for multi-circle polygon intersections achieves O(1/ε^{3/2}) complexity at O(ε) error, outperforming classical methods in experiments.
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Continuous Defensive δ-Covering is Σ²_P-complete when attacks are restricted to vertices for large δ and NP-complete when attacks can be any points on the graph.
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An improved boundary-focused adaptive quadtree algorithm for circle-polygon intersection area approximation
An adaptive quadtree algorithm with curvature-guided Monte Carlo sampling for multi-circle polygon intersections achieves O(1/ε^{3/2}) complexity at O(ε) error, outperforming classical methods in experiments.
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Continuous Defensive Domination Problems
Continuous Defensive δ-Covering is Σ²_P-complete when attacks are restricted to vertices for large δ and NP-complete when attacks can be any points on the graph.