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

scholarly journals Streaming Algorithms for Maximizing Monotone Submodular Functions Under a Knapsack Constraint

Algorithmica ◽  
2019 ◽  
Vol 82 (4) ◽  
pp. 1006-1032
Author(s):  
Chien-Chung Huang ◽  
Naonori Kakimura ◽  
Yuichi Yoshida
Keyword(s):  
Submodular Functions ◽  
Streaming Algorithms ◽  
Knapsack Constraint

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

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.

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