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Maximizing submodular+Supermodular functions Subject to a Fairness Constraint

Tsinghua Science and Technology 2024年第1期29卷 46-55页

作者： Zhenning Zhang Kaiqiao Meng Donglei Du Yang Zhou Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China Faculty of Management University of New BrunswickFredericton E3B 5A3Canada School of Mathematics and Statistics Shandong Normal UniversityJinan 250014China

We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness *** sum function is non-submodular in *** an offline model,we introduce two approximation algorithms:A greedy algorithm and a threshold greedy *** a streaming model,we propose a one-pass streaming *** also analyze the approximation ratios of these algorithms,which all depend on the total curvature of the supermodular *** total curvature is computable in polynomial time and widely utilized in the literature.

关键词： submodular function supermodular function fairness constraint greedy algorithm threshold greedy algorithm streaming algorithm

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Approximating Special Social Influence Maximization Problems

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Tsinghua Science and Technology 2020年第6期25卷 703-711页

作者： Jie Wu Ning Wang the Department of Computer and Information Sciences Temple University.PhiladelphiaPA 19122USA the Department of Computer Science Rowan UniversityGlassboroNJ 08028USA

Social Influence Maximization Problems(SIMPs)deal with selecting k seeds in a given Online Social Network(OSN)to maximize the number of eventually-influenced *** is done by using these seeds based on a given set of influence probabilities among neighbors in the *** the SIMP has been proved to be NP-hard,it has both submodular(with a natural diminishing-return)and monotone(with an increasing influenced users through propagation)that make the problem suitable for approximation ***,several special SIMPs cannot be modeled as submodular or monotone *** this paper,we look at several conditions under which non-submodular or non-monotone functions can be handled or *** is a profit-maximization SIMP where seed selection cost is included in the overall utility function,breaking the monotone *** other is a crowd-influence SIMP where crowd influence exists in addition to individual influence,breaking the submodular *** then review several new techniques and notions,including double-greedy algorithms and the supermodular degree,that can be used to address special *** main results show that for a specific SIMP model,special network structures of OSNs can help reduce its time complexity of the SIMP.

关键词： influence maximization online social networks submodular function

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An Approximation Algorithm for the Dynamic Facility Location Problem with submodular Penalties

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Acta Mathematicae Applicatae Sinica 2014年第1期30卷 187-192页

作者： Chun-yan JIANG Gai-di LI Zhen WANG Basic Courses Teaching Department The Armed Police Academy Department of Applied Mathematics Beijing University of Technology

In this paper, we study the dynamic facility location problem with submodular penalties （DFLPSP）. We present a combinatorial primal-dual 3-approximation algorithm for the DFLPSP.

关键词： dynamic facility location problem approximation algorithm submodular function

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An Approximation Algorithm for the Generalized Prize-Collecting Steiner Forest Problem with submodular Penalties

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Journal of the Operations Research Society of China 2022年第1期10卷 183-192页

作者： Xiao-Dan Jia Bo Hou Wen Liu School of Mathematical Sciences Hebei Normal UniversityShijiazhuang 050024HebeiChina

In this paper,we consider the generalized prize-collecting Steiner forest problem with submodular penalties(GPCSF-SP problem).In this problem,we are given an undirected connected graph G=(V,E)and a collection of disjoint vertex subsets V={V_(1),V_(2),…,V_(l)}.Assume c:E→R_(+)is an edge cost function andπ:2^(V)→R_(+)is a submodular penalty *** objective of the GPCSF-SP problem is to find an edge subset F such that the total cost including the edge cost in F and the penalty cost of the subcollection S containing these Vi not connected by F is *** using the primal-dual technique,we give a 3-approximation algorithm for this problem.

关键词： Generalized prize-collecting Steiner forest problem submodular function Primal-dual algorithm

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A Note on submodularity Preserved Involving the Rank functions

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Journal of the Operations Research Society of China 2019年第3期7卷 399-407页

作者： Min Li Dong-Lei Du Da-Chuan Xu Zhen-Ning Zhang School of Mathematics and Statistics Shandong Normal UniversityJinan 250358China Faculty of Business Administration University of New BrunswickFrederictonCanada College of Applied Sciences Beijing University of TechnologyBeijing 100124China

In many kinds of games with economic significance,it is very important to study the submodularity of *** this paper,wemainly study the problem of maximizing a concave function over an intersection of two *** obtain that the submod-ularity may not be preserved,but it involves one maximal submodular problem(or minimal supermodular problem)with some ***,we also present examples showing that these conditions can be satisfied.

关键词： Matroid submodular function Rank function Convexclosure Game

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