A Lower Bound of ½n² on Linear Search Programs for the Knapsack Problem

Previously the best known lower bound on this problem was 71 log 71 [I]. The result presented here is the first lower bound of better than n log n given for an NP-complete problem for a model that is actually used in practice. Previous non-linear lower bounds have been for computations involving only monotone circuits [8] or fanout limited to one. Our theorem is derived by combining results on linear search tree complexity [4] with results from threshold logic [Ill. In Section 2, we begin by presenting the results on linear search trees and threshold logic. Section 3 is devoted to using these results to obtain our main theorem.