Multilevel Algorithms for Multi-Constraint Graph Partitioning

1998 ◽  
Author(s):  
G. Karypis ◽  
V. Kumar
Keyword(s):  
Graph Partitioning ◽  
Multilevel Algorithms ◽  
Constraint Graph

Parallel static and dynamic multi-constraint graph partitioning

2002 ◽  
Vol 14 (3) ◽  
pp. 219-240 ◽  
Author(s):  
Kirk Schloegel ◽  
George Karypis ◽  
Vipin Kumar
Keyword(s):  
Graph Partitioning ◽  
Constraint Graph

A New Coarsening Strategy for Multilevel Graph Partitioning

2012 ◽  
Vol 490-495 ◽  
pp. 504-508
Author(s):  
Lu Yao ◽  
Zheng Hua Wang ◽  
Wei Cao ◽  
Zong Zhe Li
Keyword(s):  
Theoretical Analysis ◽  
Graph Partitioning ◽  
State Of The Art ◽  
Poor Quality ◽  
The State ◽  
Experimental Results ◽  
Multilevel Algorithms ◽  
Graph Partitioning Problem ◽  
Partitioning Problem ◽  
Multilevel Graph Partitioning

When applying multilevel scheme to solve the graph partitioning problem, shortcomings and limitations exist in the state-of-the-art coarsening schemes depend mainly on finding maximal matchings to obtain the coarse graphs, which can cause the multilevel algorithms to produce poor-quality solutions. This paper proposes an improved coarsening scheme by improving vertex combining strategy and edge ordering criteria. The new coarsening scheme is more effective in quality, which is proved by both theoretical analysis and experimental results.

FINAL VERSION.pdf

2019 ◽  
Author(s):  
Nasir Saeed ◽  
Mohamed-Slim Alouini ◽  
Tareq Y. Al-Naffouri
Keyword(s):  
Graph Partitioning ◽  
Three Dimensional ◽  
Smart Objects ◽  
Localization Technique ◽  
Optical Internet ◽  
Spectral Graph ◽  
Accurate Localization ◽  
Spectral Graph Partitioning ◽  
Link Connectivity

<div>Localization is a fundamental task for optical internet</div><div>of underwater things (O-IoUT) to enable various applications</div><div>such as data tagging, routing, navigation, and maintaining link connectivity. The accuracy of the localization techniques for OIoUT greatly relies on the location of the anchors. Therefore, recently localization techniques for O-IoUT which optimize the anchor’s location are proposed. However, optimization of anchors location for all the smart objects in the network is not a useful solution. Indeed, in a network of densely populated smart objects, the data collected by some sensors are more valuable than the data collected from other sensors. Therefore, in this paper, we propose a three-dimensional accurate localization technique by optimizing the anchor’s location for a set of smart objects. Spectral graph partitioning is used to select the set of valuable</div><div>sensors.</div>

Mathematics of networks

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Walks ◽  
Adjacency Matrix ◽  
Graph Partitioning ◽  
Dynamic Networks ◽  
Graph Laplacian ◽  
Network Visualization ◽  
Final Part ◽  
Bipartite Networks ◽  
Component Structure ◽  
Basic Properties

An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.

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