Improved Algorithm for Maximum Independent Set on Unit Disk Graph

2016 ◽  
pp. 212-223 ◽  
Author(s):  
Ramesh K. Jallu ◽  
Guatam K. Das
Keyword(s):  
Unit Disk ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Unit Disk Graph ◽  
Improved Algorithm

Approximation algorithms for maximum independent set of a unit disk graph

2015 ◽  
Vol 115 (3) ◽  
pp. 439-446 ◽  
Author(s):  
Gautam K. Das ◽  
Minati De ◽  
Sudeshna Kolay ◽  
Subhas C. Nandy ◽  
Susmita Sur-Kolay
Keyword(s):  
Approximation Algorithms ◽  
Unit Disk ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Unit Disk Graph

scholarly journals Faster approximation for maximum independent set on unit disk graph

2017 ◽  
Vol 127 ◽  
pp. 58-61 ◽  
Author(s):  
Subhas C. Nandy ◽  
Supantha Pandit ◽  
Sasanka Roy
Keyword(s):  
Unit Disk ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Unit Disk Graph

scholarly journals Gumbel-softmax-based optimization: a simple general framework for optimization problems on graphs

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Yaoxin Li ◽  
Jing Liu ◽  
Guozheng Lin ◽  
Yueyuan Hou ◽  
Muyun Mou ◽  
...  
Keyword(s):  
Objective Function ◽  
Statistical Physics ◽  
Automatic Differentiation ◽  
Optimization Problems ◽  
Vertex Cover ◽  
Independent Set ◽  
Computational Social Science ◽  
Maximization Problem ◽  
Maximum Independent Set ◽  
Gradient Descent Algorithm

AbstractIn computer science, there exist a large number of optimization problems defined on graphs, that is to find a best node state configuration or a network structure, such that the designed objective function is optimized under some constraints. However, these problems are notorious for their hardness to solve, because most of them are NP-hard or NP-complete. Although traditional general methods such as simulated annealing (SA), genetic algorithms (GA), and so forth have been devised to these hard problems, their accuracy and time consumption are not satisfying in practice. In this work, we proposed a simple, fast, and general algorithm framework based on advanced automatic differentiation technique empowered by deep learning frameworks. By introducing Gumbel-softmax technique, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We also introduce evolution strategy to parallel version of our algorithm. We test our algorithm on four representative optimization problems on graph including modularity optimization from network science, Sherrington–Kirkpatrick (SK) model from statistical physics, maximum independent set (MIS) and minimum vertex cover (MVC) problem from combinatorial optimization on graph, and Influence Maximization problem from computational social science. High-quality solutions can be obtained with much less time-consuming compared to the traditional approaches.

Finding a Maximum Independent Set

1977 ◽  
Vol 6 (3) ◽  
pp. 537-546 ◽  
Author(s):  
Robert Endre Tarjan ◽  
Anthony E. Trojanowski
Keyword(s):  
Independent Set ◽  
Maximum Independent Set
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