Current Status
The only known lower bound for any d is . The Overmars–Yap algorithm provides an upper bound of, so for d ≥ 3, it remains an open question whether faster algorithms are possible, or alternatively whether tighter lower bounds can be proven. In particular, it remains open whether the algorithm's running time must depend on d. In addition, the question of whether there are faster algorithms that can deal with special cases (for example, when the input coordinates are integers within a bounded range) remains open.
Read more about this topic: Klee's Measure Problem
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