Maximization of k-Submodular Function with d-Knapsack Constraints Over Sliding Window

Submodular function maximization problem has been extensively studied recently. A natural variant of submodular function is k-submodular function, which has many applications in real life, such as influence maximization and sensor placement problem. The domain of a $k$ -submodular function has $k$ disjoint subsets, and hence includes submodular function as a special case when $k=1$. This work investigates the k-submodular function maximization problem with d-knapsack constraints over the sliding window. Based on the smooth histogram technique, we design a deterministic approximation algorithm. Furthermore, we propose a randomized algorithm to improve the approximation ratio.