The equivalence of Knapsack and Waterfilling problems

Abstract

In many communications and signal processing optimization problems, the water-filling problem plays an important role in resource optimization. In this paper we show that the water-filling problem is equivalent to the classical Knapsack Problem, which is known to be NP-hard. Consequently, using the linear complexity solutions for water-filling problems and the equivalence of Knapsack Problem with water-filling problem, we present new linear time approximate solutions for Knapsack problem.