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Subquadratic submodular function minimization [PDF]
Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, 2017 Submodular function minimization (SFM) is a fundamental discrete optimization problem which generalizes many well known problems, has applications in various fields, and can be solved in polynomial time. Owing to applications in computer vision and machine learning, fast SFM algorithms are highly desirable. The current fastest algorithms [Lee, Sidford,
Chakrabarty, Deeparnab +3 more
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Submodular Functions are Noise Stable [PDF]
Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, 2012 We show that all non-negative submodular functions have high {\em noise-stability}. As a consequence, we obtain a polynomial-time learning algorithm for this class with respect to any product distribution on $\{-1,1\}^n$ (for any constant accuracy parameter $ $). Our algorithm also succeeds in the agnostic setting. Previous work on learning submodular
Cheraghchi, M +3 more
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Mathematics, 2021 In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a ...
Wencheng Wang, Xiaofei Liu
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Journal of Mathematics, 2023 In this paper, we focus on solving the vector scheduling problem with submodular penalties on parallel machines. We are given n jobs and m parallel machines, where each job is associated with a d-dimensional vector.
Bihui Cheng, Wencheng Wang
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Approximation Algorithms for the Submodular Load Balancing with Submodular Penalties
Mathematics, 2020 In this paper, we study the submodular load balancing problem with submodular penalties. The objective of this problem is to balance the load among sets, while some elements can be rejected by paying some penalties. Officially, given an element set V, we
Xiaofei Liu, Peiyin Xing, Weidong Li
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An Improved Approximation Algorithm for the Minimum Power Cover Problem with Submodular Penalty
Computation, 2022 In this paper, we consider the minimum power cover problem with submodular penalty (SPMPC). Given a set U of n users, a set S of m sensors and a penalty function π:2U→R+ on the plane, the relationship that adjusts the power p(s) of each sensor s and its ...
Han Dai
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SFExt-PGAbs: Two-Stage Summarization Model for Long Document
Jisuanji kexue yu tansuo, 2021 Aiming at the fluency problem of extractive method, the accuracy problem of abstractive method, and the important information missing problem caused by truncating the original document before document encoding, this paper proposes a two-stage long ...
ZHOU Weixiao, LAN Wenfei, XU Zhiming, ZHU Rongbo
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Submodular partition functions
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amini, Omid +3 more
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Quantitative approximation by nonlinear Angheluta-Choquet singular integrals
Journal of Numerical Analysis and Approximation Theory, 2020 By using the concept of nonlinear Choquet integral with respect to a capacity and as a generalization of the Poisson-Cauchy-Choquet operators, we introduce the nonlinear Angheluta-Choquet singular integrals with respect to a family of submodular set ...
Sorin Gal, Ionut Iancu
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A new matroid constructed by the rank function of a matroid
AKCE International Journal of Graphs and Combinatorics, 2020 In this article, we construct a submodular function using the rank function of a matroid and study induced matroid with constructed polymatroid, then we relate some properties of connectivity of new matroid with the main matroid.
Moein Pourbaba +2 more
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