Streaming Submodular Maximization Under Matroid Constraints

• 成果类型: Article; Early Access
• 署名作者: Feldman, Moran; Liu, Paul; Norouzi-Fard, Ashkan; Svensson, Ola; Zenklusen, Rico
• 署名单位: University of Haifa; Stanford University; Alphabet Inc.; Google Incorporated; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0276
• 发表日期: 2025

摘要

Recent progress in (semi-)streaming algorithms for monotone submodular function maximization has led to tight results for a simple cardinality constraint. However, current techniques fail to give a similar understanding for natural generalizations, including matroid constraints. This paper aims at closing this gap. For a single matroid of rank k (i.e., any solution has cardinality at most k), our main results are a single-pass streaming algorithm that uses Oe(k) memory and achieves an approximation guarantee of 0.3178 and a multipass streaming algorithm that uses Oe(k) memory and achieves an approximation guarantee of (1- 1/e- E) by taking a constant (depending on E) number of passes over the stream. This improves on the previously best approximation guarantees of 1/4 and 1/2 for single-pass and multipass streaming algorithms, respectively. In fact, our multipass streaming algorithm is tight in that any algorithm with a better guarantee than 1/2 must make several passes through the stream and any algorithm that beats our guarantee of 1- 1/e must make linearly many passes (as well as an exponential number of value oracle queries). Moreover, we show how the approach that we use for multipass streaming can be further strengthened if the elements of the stream arrive in uniformly random order, implying an improved result for p-matchoid constraints.