Lower Bounds on Time-Accuracy Trade-Offs for the 0-1 Knapsack Problem

The 0-1 Knapsack optimization problem is well known to be NP-hard. The best known approximation algorithms for this problem are approximation schemes which exhibit trade-offs between the running time of the algorithm and the guaranteed accuracy of the solution. This paper establishes lower bounds on the time required to find approximate solutions of guaranteed accuracy for a class of knapsack algorithms which must use oracles to perform feasibility tests and dominance tests.