Randomized Complexity Lower Bound for Arrangements and Polyhedra
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The complexity lower bound Ω (log N ) for randomized computation trees is proved for recognizing an arrangement or a polyhedron with N faces. This provides, in particular, the randomized lower bound Ω (n log n ) for the DISTINCTNESS problem and generalizes  where the randomized lower bound Ω (n 2 ) was ascertained for the KNAPSACK problem. The core of the method is an extension of the lower bound from  on the multiplicative complexity of a polynomial.