Maximizing DR-submodular+supermodular functions on the integer lattice subject to a cardinality constraint

2021 ◽  
Author(s):  
Zhenning Zhang ◽  
Donglei Du ◽  
Yanjun Jiang ◽  
Chenchen Wu
Keyword(s):  
Integer Lattice ◽  
Cardinality Constraint ◽  
Supermodular Functions

Monotone submodular maximization over the bounded integer lattice with cardinality constraints

2019 ◽  
Vol 11 (06) ◽  
pp. 1950075
Author(s):  
Lei Lai ◽  
Qiufen Ni ◽  
Changhong Lu ◽  
Chuanhe Huang ◽  
Weili Wu
Keyword(s):  
Approximation Algorithm ◽  
Greedy Algorithm ◽  
Deterministic Algorithm ◽  
Submodular Function ◽  
Integer Lattice ◽  
Cardinality Constraint ◽  
Cardinality Constraints ◽  
Definition Of ◽  
Deterministic Formula ◽  
Submodular Maximization

We consider the problem of maximizing monotone submodular function over the bounded integer lattice with a cardinality constraint. Function [Formula: see text] is submodular over integer lattice if [Formula: see text], [Formula: see text], where ∨ and ∧ represent elementwise maximum and minimum, respectively. Let [Formula: see text], and [Formula: see text], we study the problem of maximizing submodular function [Formula: see text] with constraints [Formula: see text] and [Formula: see text]. A random greedy [Formula: see text]-approximation algorithm and a deterministic [Formula: see text]-approximation algorithm are proposed in this paper. Both algorithms work in value oracle model. In the random greedy algorithm, we assume the monotone submodular function satisfies diminishing return property, which is not an equivalent definition of submodularity on integer lattice. Additionally, our random greedy algorithm makes [Formula: see text] value oracle queries and deterministic algorithm makes [Formula: see text] value oracle queries.

Characterizing Mixability of Supermodular Functions

2014 ◽  
Author(s):  
Valeria Bignozzi ◽  
Giovanni Puccetti
Keyword(s):  
Supermodular Functions

An Efficient Bounds Consistency Algorithm for the Global Cardinality Constraint

Constraints ◽  
2005 ◽  
Vol 10 (2) ◽  
pp. 115-135 ◽  
Author(s):  
Claude-Guy Quimper ◽  
Alexander Golynski ◽  
Alejandro López-Ortiz ◽  
Peter Van Beek
Keyword(s):  
Cardinality Constraint

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

CELLULAR NEURAL NETWORKS: ASYMMETRIC SPACE-DEPENDENT TEMPLATES, MOSAIC PATTERNS, AND SPATIAL CHAOS

2004 ◽  
Vol 14 (08) ◽  
pp. 2655-2665 ◽  
Author(s):  
LARRY TURYN
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Hexagonal Lattice ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Integer Lattice ◽  
Spatial Entropy ◽  
Spatial Chaos

We consider a Cellular Neural Network (CNN), with a bias term, on the integer lattice ℤ2in the plane ℝ2. Space-dependent, asymmetric couplings (templates) appropriate for CNN in the hexagonal lattice on ℝ2are studied. We characterize the mosaic patterns and study their spatial entropy. It appears that for this problem, asymmetry of the template has a more robust effect on the spatial entropy than does the sign of a parameter in the templates.

Nonsubmodular Constrained Profit Maximization in Attribute Networks

2021 ◽  
Author(s):  
Liman Du ◽  
Wenguo Yang ◽  
Suixiang Gao
Keyword(s):  
Profit Maximization ◽  
Logistic Function ◽  
Influence Maximization ◽  
Maximization Problem ◽  
Cardinality Constraint ◽  
Three Phase ◽  
Marginal Increment ◽  
The Difference ◽  
Classical Influence ◽  
Influence Maximization Problem

The number of social individuals who interact with their friends through social networks is increasing, leading to an undeniable fact that word-of-mouth marketing has become one of the useful ways to promote sale of products. The Constrained Profit Maximization in Attribute network (CPMA) problem, as an extension of the classical influence maximization problem, is the main focus of this paper. We propose the profit maximization in attribute network problem under a cardinality constraint which is closer to the actual situation. The profit spread metric of CPMA calculates the total benefit and cost generated by all the active nodes. Different from the classical Influence Maximization problem, the influence strength should be recalculated according to the emotional tendency and classification label of nodes in attribute networks. The profit spread metric is no longer monotone and submodular in general. Given that the profit spread metric can be expressed as the difference between two submodular functions and admits a DS decomposition, a three-phase algorithm named as Marginal increment and Community-based Prune and Search(MCPS) Algorithm frame is proposed which is based on Louvain algorithm and logistic function. Due to the method of marginal increment, MPCS algorithm can compute profit spread more directly and accurately. Experiments demonstrate the effectiveness of MCPS algorithm.

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