Bringing Order to Special Cases of Klee's Measure Problem

Klee’s Measure Problem (KMP) asks for the volume of the union of n axis-aligned boxes in ℝ d . Omitting logarithmic factors, the best algorithm has runtime \(\mathcal{O}^*(n^{d/2})\) [Overmars,Yap’91]. There are faster algorithms known for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP (where all boxes are cubes of equal side length), Hypervolume (where all boxes share a vertex), and k -Grounded (where the projection onto the first k dimensions is a Hypervolume instance).

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