Maximize an Approximate K-Submodular Function under a Knapsack Constraint.

In this paper, we consider the problem of maximizing a monotone approximate k-submodular function under a knapsack constraint. For monotone approximate k-submodular functions, we characterize the approximately k-submodular degree by k-submodularity ratio and present a γ/1+γ·( 1-e^-1) greedy approximation algorithm under a knapsack constraint.