Under Gap-ETH, the n^{O(1/ε^{d-1})}-time shifting PTAS is optimal for maximum independent set, minimum dominating set, maximum induced forest, maximum induced matching, and minimum piercing set on unit ball graphs in every constant dimension d≥2.
Agarwal and Cecilia Magdalena Procopiuc
3 Pith papers cite this work, alongside 246 external citations. Polarity classification is still indexing.
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MSR is W[1]-hard parameterized by k+Delta on weighted bipartite graphs and by vertex cover number plus k, but FPT parameterized by treewidth plus Delta on weighted graphs.
Smallest-enclosing-disk queries over points in axis-aligned rectangles can be answered in O(log^4 n) deterministic or O(log^{5/2} n log log n) expected time via 2D farthest-point Voronoi diagrams.
citing papers explorer
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Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes
Under Gap-ETH, the n^{O(1/ε^{d-1})}-time shifting PTAS is optimal for maximum independent set, minimum dominating set, maximum induced forest, maximum induced matching, and minimum piercing set on unit ball graphs in every constant dimension d≥2.
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On the Parameterized Complexity of Min-Sum-Radii
MSR is W[1]-hard parameterized by k+Delta on weighted bipartite graphs and by vertex cover number plus k, but FPT parameterized by treewidth plus Delta on weighted graphs.
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Smallest Enclosing Disk Queries Using Farthest-Point Voronoi Diagrams
Smallest-enclosing-disk queries over points in axis-aligned rectangles can be answered in O(log^4 n) deterministic or O(log^{5/2} n log log n) expected time via 2D farthest-point Voronoi diagrams.