Randomized Complexity Lower Bound for Arrangements and Polyhedra

D. Grigoriev
1999 Discrete & Computational Geometry  
The complexity lower bound (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 (n log n) for the DISTINCTNESS problem and generalizes 11] where the randomized lower bound (n 2 ) was ascertained for the KNAPSACK problem. The core of the method is an extension of the lower bound from 8] on the multiplicative complexity of a polynomial.
doi:10.1007/pl00009425 fatcat:bptptvesw5f27kp62ds3lltp2e