Maximizing a monotone non-submodular function under a knapsack constraint

Submodular optimization has been well studied in combinatorial optimization. However, there are few works considering about non-submodular optimization problems which also have many applications, such as experimental design, some optimization problems in social networks, etc. In this paper, we consider the maximization of non-submodular function under a knapsack constraint, and explore the performance of the greedy algorithm, which is characterized by the submodularity ratio beta and curvature alpha. In particular, we prove that the greedy algorithm enjoys a tight approximation guarantee of (1 - e(-alpha beta))/alpha for the above problem. To our knowledge, it is the first tight constant factor for this problem. We further utilize illustrative examples to demonstrate the performance of our algorithm.

Automated summary

This paper investigates the maximization of non-submodular function under a knapsack constraint and explores the performance of the greedy algorithm. The authors provide a tight approximation guarantee for the greedy algorithm, which fills the gap in this area and is the first of its kind for this problem. Illustrative examples are used to demonstrate the performance of the algorithm.