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Randomized Parallel Algorithm for Maximizing Nonsubmodular Function Subject to Cardinality Constraint

Author

Listed:
  • Jingjing Tan

    (School of Mathematics and Information Science, Weifang University, Weifang Shandong, 261061, P. R. China)

  • Wenting Chen

    (School of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao Shandong 266590, P. R. China)

  • Meixia Li

    (School of Mathematics and Information Science, Weifang University, Weifang Shandong, 261061, P. R. China)

  • Wenchao Wang

    (School of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao Shandong 266590, P. R. China)

Abstract

The problem of maximization submodular functions with a cardinality constraint has been extensively researched in recent years. Balkanski and Singer were the first to study this class problem. Subsequently, Chekuri and Kent recently extended these results to more general constraints, that is, k-cardinality constraint, partition and laminar matroids, matching, knapsack constraints, and including their intersection. They proposed a (1 āˆ’ 1/e āˆ’ šœ€) approximation randomized-parallel-greedy algorithm which are poly-logarithmic adaptivity. However, these existing approaches are hardly extended to the nonsubmodular case. In this paper, we investigate the problem of maximization on a nonsubmodular function subject to a cardinality constraint, provided the objective function is specified by a generic submodularity ratio Ī³. We design a (1 āˆ’ eāˆ’Ī³ āˆ’ šœ€)-approximation Greedy algorithm by using the technical aspects to maximize the multilinear relaxation of the object function under the k-cardinality constraints. The adaptive of multilinear relaxation is O(log n/šœ€2); the number of oracle is ƕ(n/šœ€4).

Suggested Citation

  • Jingjing Tan & Wenting Chen & Meixia Li & Wenchao Wang, 2021. "Randomized Parallel Algorithm for Maximizing Nonsubmodular Function Subject to Cardinality Constraint," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(05), pages 1-11, October.
  • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:05:n:s0217595921400091
    DOI: 10.1142/S0217595921400091
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