The hardness of approximating set cover

1998 ◽  
pp. 249-262
Author(s):  
Alexander Wolff
Keyword(s):  
Set Cover

PE-MSC: partial entailment-based minimum set cover for text summarization

2021 ◽  
Author(s):  
Anand Gupta ◽  
Manpreet Kaur ◽  
Sonaali Mittal ◽  
Swati Garg
Keyword(s):  
Text Summarization ◽  
Set Cover

Calculating approximation guarantees for partial set cover of pairs

2017 ◽  
Vol 11 (7) ◽  
pp. 1293-1302 ◽  
Author(s):  
Peter Damaschke
Keyword(s):  
Set Cover

scholarly journals Improved analysis of the online set cover problem with advice

2017 ◽  
Vol 689 ◽  
pp. 96-107 ◽  
Author(s):  
Stefan Dobrev ◽  
Jeff Edmonds ◽  
Dennis Komm ◽  
Rastislav Královič ◽  
Richard Královič ◽  
...  
Keyword(s):  
Set Cover ◽  
Set Cover Problem ◽  
Cover Problem

The Star Degree Centrality Problem: A Decomposition Approach

2021 ◽  
Author(s):  
Mustafa C. Camur ◽  
Thomas Sharkey ◽  
Chrysafis Vogiatzis
Keyword(s):  
Integer Programming ◽  
Large Scale ◽  
Benders Decomposition ◽  
Open Neighborhood ◽  
Decomposition Algorithm ◽  
Solution Time ◽  
Set Cover ◽  
Degree Centrality ◽  
Decomposition Approach ◽  
Acceleration Techniques

We consider the problem of identifying the induced star with the largest cardinality open neighborhood in a graph. This problem, also known as the star degree centrality (SDC) problem, is shown to be [Formula: see text]-complete. In this work, we first propose a new integer programming (IP) formulation, which has a smaller number of constraints and nonzero coefficients in them than the existing formulation in the literature. We present classes of networks in which the problem is solvable in polynomial time and offer a new proof of [Formula: see text]-completeness that shows the problem remains [Formula: see text]-complete for both bipartite and split graphs. In addition, we propose a decomposition framework that is suitable for both the existing and our formulations. We implement several acceleration techniques in this framework, motivated by techniques used in Benders decomposition. We test our approaches on networks generated based on the Barabási–Albert, Erdös–Rényi, and Watts–Strogatz models. Our decomposition approach outperforms solving the IP formulations in most of the instances in terms of both solution time and quality; this is especially true for larger and denser graphs. We then test the decomposition algorithm on large-scale protein–protein interaction networks, for which SDC is shown to be an important centrality metric. Summary of Contribution: In this study, we first introduce a new integer programming (NIP) formulation for the star degree centrality (SDC) problem in which the goal is to identify the induced star with the largest open neighborhood. We then show that, although the SDC can be efficiently solved in tree graphs, it remains [Formula: see text]-complete in both split and bipartite graphs via a reduction performed from the set cover problem. In addition, we implement a decomposition algorithm motivated by Benders decomposition together with several acceleration techniques to both the NIP formulation and the existing formulation in the literature. Our experimental results indicate that the decomposition implementation on the NIP is the best solution method in terms of both solution time and quality.

Randomized Online Algorithms for Set Cover Leasing Problems

2014 ◽  
pp. 25-34 ◽  
Author(s):  
Sebastian Abshoff ◽  
Christine Markarian ◽  
Friedhelm Meyer auf der Heide
Keyword(s):  
Online Algorithms ◽  
Set Cover
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