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
Famous quotes containing the words current and/or status:
“Gradually the village murmur subsided, and we seemed to be embarked on the placid current of our dreams, floating from past to future as silently as one awakes to fresh morning or evening thoughts.”
—Henry David Thoreau (1817–1862)
“As a work of art it has the same status as a long conversation between two not very bright drunks.”
—Clive James (b. 1939)