On streaming algorithms for maximizing a supermodular function plus a MDR-submodular function on the integer lattice

Jingjing Tan, Yicheng Xu (), Dongmei Zhang and Xiaoqing Zhang
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Jingjing Tan: Weifang University
Yicheng Xu: Chinese Academy of Sciences
Dongmei Zhang: Shandong Jianzhu University
Xiaoqing Zhang: Beijing University of Technology

Journal of Combinatorial Optimization, 2023, vol. 45, issue 2, No 1, 19 pages

Abstract: Abstract In this paper, we provide a streaming algorithm for the problem of maximizing the sum of a supermodular function and a nonnegative monotone diminishing return submodular (MDR-submodular) function with a knapsack constraint on the integer lattice. Inspired by the SIEVE-STREAMING algorithm, we present a two-pass streaming algorithm by using the threshold technique. Then, we improve the two-pass streaming algorithm to one-pass and further reduce its space complexity. The proposed algorithms are proved to have polynomial time and space complexity, and a performance guarantee dependent on the curvature of the supermodular function. Finally, we carry out numerical experiments to verify the performance of the algorithm.

Keywords: DR-submodular function; Supermodular function; Knapsack constraint; Threshold greedy algorithm; Integer lattice (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-00986-y

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