An almost optimal approximation algorithm for monotone submodular multiple knapsack

We study the problem of maximizing a monotone submodular function subject to Multiple Knapsack constraint. The input is set I items, each has non-negative weight, and bins arbitrary capacities. Also, we are given submodular, f over subsets items. objective find packing subset items A⊆I in such that f(A) maximized. Our main result an almost optimal polynomial time (1−e−1−ε)-approximation algorithm for problem, any ε>0. relies on structuring technique which converts general multiple knapsack constraint partitioned into groups exponentially increasing cardinalities, consisting uniform capacity. derive by combining with refined analysis techniques optimization constraints.