Multi-Pass Streaming Algorithms for Monotone Submodular Function Maximization

We consider maximizing a monotone submodular function under cardinality constraint or knapsack in the streaming setting. In particular, elements arrive sequentially and at any point of time, algorithm has access to only small fraction data stored primary memory. propose following algorithms taking O(ε− 1) passes: (1) (1 − e− 1 ε)-approximation for cardinality-constrained problem, (2) (0.5 knapsack-constrained problem. Both our run deterministically O∗(n) using O∗(K) space, where n is size ground set K knapsack. Here term O∗ hides polynomial $\log K$ ε− 1. Our can also be used as fast approximation algorithms. takes $O(n\varepsilon ^{-1} \log (\varepsilon ^{-1}\log K) )$ improving on Badanidiyuru Vondrák that $O(n \varepsilon time.