Improvable Knapsack Problems

Goerigk, Marc and Sabharwal, Yogish and Schöbel, Anita and Sen, Sandeep (2016) Improvable Knapsack Problems. Working Paper. UNSPECIFIED.

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.