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### Paper:

TR96-058 | 25th November 1996 00:00

#### Randomized $\mathbf{\Omega (n^2)}$ Lower Bound for Knapsack

TR96-058
Authors: Dima Grigoriev, Marek Karpinski
Publication: 25th November 1996 13:48
Keywords:

Abstract:

We prove $\Omega (n^2)$ complexity \emph{lower bound} for the
general model of \emph{randomized computation trees} solving
the \emph{Knapsack Problem}, and more generally \emph{Restricted
Integer Programming}. This is the \emph{first nontrivial} lower
bound proven for this model of computation. The method of the
proof depends crucially on the new technique for proving lower
bounds on the \emph{border complexity} of a polynomial which
could be of independent interest.

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