Structural theorems for submodular functions, polymatroids and polymatroid intersections

1988 ◽  
Vol 4 (1) ◽  
pp. 257-284 ◽  
Author(s):  
Masataka Nakamura
Keyword(s):  
Submodular Functions ◽  
Structural Theorems

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.

Structural theorems for multiplicative systems of functions

1985 ◽  
Vol 46 (1-2) ◽  
pp. 111-127
Author(s):  
J. Jakubowski
Keyword(s):  
Multiplicative Systems ◽  
Structural Theorems

scholarly journals Maximizing k -Submodular Functions and Beyond

2016 ◽  
Vol 12 (4) ◽  
pp. 1-26 ◽  
Author(s):  
Justin Ward ◽  
Stanislav Živný
Keyword(s):  
Submodular Functions

Maximizing Non-monotone Submodular Functions

2011 ◽  
Vol 40 (4) ◽  
pp. 1133-1153 ◽  
Author(s):  
Uriel Feige ◽  
Vahab S. Mirrokni ◽  
Jan Vondrák
Keyword(s):  
Submodular Functions
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