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Article Dans Une Revue Algorithmica Année : 2021

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

Résumé

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

hal-03456727 , version 1 (24-03-2022)

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Chien-Chung Huang, Naonori Kakimura. Improved Streaming Algorithms for Maximizing Monotone Submodular Functions under a Knapsack Constraint. Algorithmica, 2021, 83 (3), pp.879-902. ⟨10.1007/s00453-020-00786-4⟩. ⟨hal-03456727⟩
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