scholarly journals Maximizing monotone submodular functions over the integer lattice

2018 ◽  
Vol 172 (1-2) ◽  
pp. 539-563 ◽  
Author(s):  
Tasuku Soma ◽  
Yuichi Yoshida
Keyword(s):  
Integer Lattice ◽  
Submodular Functions

Streaming Algorithms for Maximizing Non-submodular Functions on the Integer Lattice

2021 ◽  
pp. 3-14
Author(s):  
Bin Liu ◽  
Zihan Chen ◽  
Huijuan Wang ◽  
Weili Wu
Keyword(s):  
Integer Lattice ◽  
Submodular Functions ◽  
Streaming Algorithms

A fast double greedy algorithm for non-monotone DR-submodular function maximization

2019 ◽  
Vol 12 (01) ◽  
pp. 2050007 ◽  
Author(s):  
Shuyang Gu ◽  
Ganquan Shi ◽  
Weili Wu ◽  
Changhong Lu
Keyword(s):  
Machine Learning ◽  
Greedy Algorithm ◽  
Submodular Function ◽  
Integer Lattice ◽  
Submodular Functions ◽  
Running Time ◽  
Submodular Function Maximization ◽  
Multiple Copies ◽  
Submodular Set Function ◽  
Set Function

We study the problem of maximizing non-monotone diminish return (DR)-submodular function on the bounded integer lattice, which is a generalization of submodular set function. DR-submodular functions consider the case that we can choose multiple copies for each element in the ground set. This generalization has many applications in machine learning. In this paper, we propose a [Formula: see text]-approximation algorithm with a running time of [Formula: see text], where [Formula: see text] is the size of the ground set, [Formula: see text] is the upper bound of integer lattice. Discovering important properties of DR-submodular function, we propose a fast double greedy algorithm which improves the running time.

scholarly journals Evolutionary algorithms and submodular functions: benefits of heavy-tailed mutations

2021 ◽  
Author(s):  
Francesco Quinzan ◽  
Andreas Göbel ◽  
Markus Wagner ◽  
Tobias Friedrich
Keyword(s):  
Evolutionary Algorithms ◽  
Submodular Functions ◽  
Heavy Tailed

scholarly journals Non-submodular model for group profit maximization problem in social networks

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Jianming Zhu ◽  
Smita Ghosh ◽  
Weili Wu ◽  
Chuangen Gao
Keyword(s):  
Social Networks ◽  
Profit Maximization ◽  
Randomized Algorithm ◽  
Political Orientation ◽  
Submodular Functions ◽  
Maximization Problem ◽  
Modular Algorithm ◽  
The Difference ◽  
Group Enterprise ◽  
Theoretical Results

AbstractIn social networks, there exist many kinds of groups in which people may have the same interests, hobbies, or political orientation. Sometimes, group decisions are made by simply majority, which means that most of the users in this group reach an agreement, such as US Presidential Elections. A group is called activated if $$\beta$$ β percent of users are influenced in the group. Enterprise will gain income from all influenced groups. Simultaneously, to propagate influence, enterprise needs pay advertisement diffusion cost. Group profit maximization (GPM) problem aims to pick k seeds to maximize the expected profit that considers the benefit of influenced groups with the diffusion cost. GPM is proved to be NP-hard and the objective function is proved to be neither submodular nor supermodular. An upper bound and a lower bound which are difference of two submodular functions are designed. We propose a submodular–modular algorithm (SMA) to solve the difference of two submodular functions and SMA is shown to converge to a local optimal. We present an randomized algorithm based on weighted group coverage maximization for GPM and apply sandwich framework to get theoretical results. Our experiments verify the efficiency of our methods.

scholarly journals Routing sets in the integer lattice

2007 ◽  
Vol 155 (11) ◽  
pp. 1384-1394 ◽  
Author(s):  
Peter Hamburger ◽  
Robert Vandell ◽  
Matt Walsh
Keyword(s):  
Integer Lattice
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