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Bringing Order to Special Cases of Klee's Measure Problem
[chapter]
2013
Lecture Notes in Computer Science
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 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). In this
doi:10.1007/978-3-642-40313-2_20
fatcat:xedlkxowwffvljfpfhtw7b5fi4