Approximation algorithms on 01 linear knapsack problem with a single continuous variable
The 01 linear knapsack problem with a single continuous variable (KPC) is a natural generalization of the standard 01 linear knapsack problem (KP). In KPC, the capacity of the knapsack is not fixed, but can be adjusted by a continuous variable. This paper studies the approximation algorithm on KPC. Firstly, assuming that the weight of each item is at most the original capacity of the knapsack, we give a 2-approximation algorithm on KPC by generalizing the 2-approximation algorithm on KP. Then, without the above assumption, we give another 2-approximation algorithm on KPC for general cases by extending the first algorithm.
approximation algorithm knapsack single continuous variable