A k-submodular function is an extension of a submodular function in that its input is given by k disjoint subsets instead of a single subset. For unconstrained nonnegative k-submodular maximization, Ward and Živný proposed a constant-factor approximation algorithm, which was improved by the recent work of Iwata, Tanigawa and Yoshida presenting a 1/2-approximation algorithm. Iwata et al. also provided a k/(2k−1)
Nearby in the stack
-approximation algorithm for monotone
k
-submodular maximization and proved that its approximation ratio is asymptotically tight. More recently, Ohsaka and Yoshida proposed constant-factor algorithms for monotone
k
-submodular maximization with several size constraints. However, while submodular maximization with various constraints has been extensively studied, no approximation algorithm has been developed for constrained
k
-submodular maximization, except for the case of size constraints. In this paper, we prove that a greedy algorithm outputs a
1/2
-approximate solution for monotone
k
-submodular maximization with a matroid constraint. The algorithm runs in
O(M∣E∣(MO+kEO))
time, where
M
is the size of a maximal optimal solution,
∣E∣
is the size of the ground set, and
MO,EO
represent the time for the membership oracle of the matroid and the evaluation oracle of the