scholarly journals Cascade Submodular Maximization: Question Selection and Sequencing in Online Personality Quiz

2021 ◽  
Author(s):  
Shaojie Tang ◽  
Jing Yuan
Keyword(s):  
Question Selection ◽  
Submodular Maximization

scholarly journals Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint

2021 ◽  
Vol 5 (1) ◽  
pp. 1-22
Author(s):  
Jing Tang ◽  
Xueyan Tang ◽  
Andrew Lim ◽  
Kai Han ◽  
Chongshou Li ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Greedy Algorithm ◽  
Branch And Bound ◽  
Upper Bound ◽  
Optimization Problem ◽  
Approximation Factor ◽  
Real World Application ◽  
Efficiency Of Algorithms ◽  
Knapsack Constraint ◽  
Submodular Maximization

Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we show that this algorithm can achieve an approximation factor of 0.405, which significantly improves the known factors of 0.357 given by Wolsey and (1-1/e)/2\approx 0.316 given by Khuller et al. More importantly, our analysis closes a gap in Khuller et al.'s proof for the extensively mentioned approximation factor of (1-1/\sqrte )\approx 0.393 in the literature to clarify a long-standing misconception on this issue. Second, we enhance the modified greedy algorithm to derive a data-dependent upper bound on the optimum. We empirically demonstrate the tightness of our upper bound with a real-world application. The bound enables us to obtain a data-dependent ratio typically much higher than 0.405 between the solution value of the modified greedy algorithm and the optimum. It can also be used to significantly improve the efficiency of algorithms such as branch and bound.

scholarly journals Deterministic Algorithms for Submodular Maximization Problems

2018 ◽  
Vol 14 (3) ◽  
pp. 1-20 ◽  
Author(s):  
Niv Buchbinder ◽  
Moran Feldman
Keyword(s):  
Deterministic Algorithms ◽  
Submodular Maximization

Two-stage submodular maximization problem beyond nonnegative and monotone

2021 ◽  
pp. 1-16
Author(s):  
Zhicheng Liu ◽  
Hong Chang ◽  
Ran Ma ◽  
Donglei Du ◽  
Xiaoyan Zhang
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Objective Function ◽  
Modular Function ◽  
Submodular Function ◽  
Maximization Problem ◽  
Cardinality Constraint ◽  
Two Stage ◽  
Time Efficiency ◽  
Submodular Maximization

Abstract We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right),1} \right)$ -approximation algorithm, and the second is a randomized $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right) - \varepsilon ,1} \right)$ -approximation algorithm with improved time efficiency.

An Intelligent Framework for Automatic Question Set Generation

2011 ◽  
pp. 168-177
Author(s):  
Joydip Dhar ◽  
Abhishek Vaid ◽  
Manyata Goyal ◽  
Shilp Gupta
Keyword(s):  
Selection Process ◽  
Classification Problem ◽  
Design Parameters ◽  
Feature Maps ◽  
Test Management ◽  
Novel Technique ◽  
Online Test ◽  
Question Classification ◽  
Question Selection ◽  
Future Direction

Automated question selection is an emerging problem in the industry of Online Test Management. The Test Management Suites, offer administration of question sets, either precompiled by experts, or randomized over the database of questions. Presently available literature in this domain is sparse and primarily focuses on automated question classification problem. This paper proposes a novel technique for administering question sets in an intelligent and automated approach. Artificial Intelligence, in the form of Self Organizing Feature Maps is utilized for question selection process. Finally, results from experiments are compiled for an illustration of the whole technique. Optimal design parameters for further research are also proposed alongside plausible future direction in pervasive computing.

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