Submodular function maximization has been a central topic in the theoretical
computer science community over the last decade. Plenty of well-performing
approximation algorithms have been designed for the maximization of (monotone
or non-monotone) submodular functions over a variety of constraints. In this
paper, we consider the submodular multiple knapsack problem (SMKP), which is
the submodular version of the well-studied multiple knapsack problem (MKP).
Roughly speaking, the problem asks to maximize a monotone submodular function
over multiple bins (knapsacks). Recently, Fairstein et al. (ESA20) presented a
tight (1β1/eβΟ΅)-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. In this paper, we present a tight
(1β1/eβΟ΅) deterministic algorithm for SMKP. Our algorithm is based on
reducing SMKP to an exponential-size submodular maximizaion problem over a
special partition matroid which enjoys a tight deterministic algorithm. We
develop several techniques to mimic the algorithm, leading to a tight
deterministic approximation for SMKP