Improved Streaming Algorithms for Maximizing Monotone Submodular Functions under a Knapsack Constraint

In this paper, we consider the problem of maximizing a monotone submodular function subject to knapsack constraint in streaming setting. such setting, elements arrive sequentially and at any point time, algorithm can store only small fraction that have arrived so far. For special case all unit sizes (i.e., cardinality-constraint case), one find $$(0.5-\varepsilon )$$ -approximate solution $$O(K\varepsilon ^{-1})$$ space, where K is capacity (Badanidiyuru et al. KDD 2014). The approximation ratio recently shown be optimal (Feldman STOC 2020). work, propose $$(0.4-\varepsilon -approximation for knapsack-constrained problem, using space polynomial $$\varepsilon $$ . This improves on previous best $$0.363-\varepsilon with same order. Our based careful combination various ideas transform multiple-pass algorithms into single-pass one.