Approximation of the Quadratic Knapsack Problem

TL;DR

This paper presents an algorithm for the Quadratic Knapsack Problem that achieves a specific approximation ratio and runtime, advancing the computational methods for this complex optimization problem.

Contribution

The paper introduces a novel algorithm with provable approximation bounds and runtime for the Quadratic Knapsack Problem, a significant step forward in combinatorial optimization.

Findings

Approximation ratio within O(n^{2/5+ε})

Runtime within O(n^{9/ε})

Applicable for any ε > 0

Abstract

For any given $\epsilon>0$ we provide an algorithm for the Quadratic Knapsack Problem that has an approximation ratio within $O(n^{2/5+\epsilon})$ and a run time within $O(n^{9/\epsilon})$.