Improvable Knapsack Problems

TL;DR

This paper investigates a variant of the knapsack problem where items can be improved with a separate budget, providing approximation algorithms and PTAS for various cases to maximize profit.

Contribution

It introduces and analyzes improvable knapsack problems, offering new approximation algorithms and PTAS for different scenarios.

Findings

Constant factor approximation algorithms developed

Two PTAS proposed for specific cases

Enhanced understanding of improvable knapsack problem complexity

Abstract

We consider a variant of the knapsack problem, where items are available with different possible weights. Using a separate budget for these item improvements, the question is: Which items should be improved to which degree such that the resulting classic knapsack problem yields maximum profit? We present a detailed analysis for several cases of improvable knapsack problems, presenting constant factor approximation algorithms and two PTAS.