A k-submodular function is a generalization of the submodular set function. Many practical applications can be modeled as maximizing a k-submodular function, such as multi-cooperative games, sensor placement with k type sensors, influence maximization with k topics, and feature selection with k partitions. In this paper, we provide a unified continuous greedy algorithm for k
Nearby in the stack
-submodular maximization problem under a down-monotone constraint. Our technique involves relaxing the discrete variables in a continuous space by using the multilinear extension of
k
-submodular function to find a fractional solution, and then rounding it to obtain the feasible solution. Our proposed algorithm runs in polynomial time and can be applied to both the non-monotone and monotone cases. When the objective function is non-monotone, our algorithm achieves an approximation ratio of
(1/e−o(1))
; for a monotone
k
-submodular objective function, it achieves an approximation ratio of