Before revision:  Despite lots of known results in the field of submodular maximization, surprisingly, it remains unknown whether or not this problem enjoys the well-known tight (1 - 1 / e )-approximation .
After revision:  Despite lots of known results in the field of submodular maximization, surprisingly, it remains unknown whether or not this problem enjoys the well-known tight (1 - 1 / e )-approximation randomized algorithm for SMKP. Their algorithm is based on the continuous greedy technique which inherently involves randomness. However, the deterministic algorithm of this problem has not been understood very well previously.