We study an extension of the cardinality-constrained knapsack problem where each item has a concave piecewise-linear utility structure. Our main contributions are approximation algorithms for the problem and the investigation of an online version in the random order model. For the offline...

We investigate the problem of $k$-submodular maximization under a knapsack constraint over the ground set of size $n$. This problem finds many applications in various fields such as multi-topic propagation, multi-sensor placement, cooperative games, etc. However, existing algorithms for the...