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 a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary memory. For this problem, we propose a (0.363− ε)-approximation algorithm, requiring only a single pass through the data; moreover, we propose a (0.4 − ε)-approximation algorithm requiring a constant number of passes through the data. The required memory space of both algorithms depends only on the size of the knapsack capacity and ε. 1998 ACM Subject Classification G.2.1 Combinatorics