Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

State of the art document clustering algorithms based on semantic similarity

The constant success of the Internet made the number of text documents in electronic forms increases hugely. The techniques to group these documents into meaningful clusters are becoming critical missions. The traditional clustering method was based on statistical features, and the clustering was done using a syntactic notion rather than semantically. However, these techniques resulted in un-similar data gathered in the same group due to polysemy and synonymy problems. The important solution to this issue is to document clustering based on semantic similarity, in which the documents are grouped according to the meaning and not keywords. In this research, eighty papers that use semantic similarity in different fields have been reviewed; forty of them that are using semantic similarity based on document clustering in seven recent years have been selected for a deep study, published between the years 2014 to 2020. A comprehensive literature review for all the selected papers is stated. Detailed research and comparison regarding their clustering algorithms, utilized tools, and methods of evaluation are given. This helps in the implementation and evaluation of the clustering of documents. The exposed research is used in the same direction when preparing the proposed research. Finally, an intensive discussion comparing the works is presented, and the result of our research is shown in figures

Graph partitioning algorithms for optimizing software deployment in mobile cloud computing

As cloud computing is gaining popularity, an important question is how to optimally deploy software applications on the offered infrastructure in the cloud. Especially in the context of mobile computing where software components could be offloaded from the mobile device to the cloud, it is important to optimize the deployment, by minimizing the network usage. Therefore we have designed and evaluated graph partitioning algorithms that allocate software components to machines in the cloud while minimizing the required bandwidth. Contrary to the traditional graph partitioning problem our algorithms are not restricted to balanced partitions and take into account infrastructure heterogenity. To benchmark our algorithms we evaluated their performance and found they produce 10 to 40 % smaller graph cut sizes than METIS 4.0 for typical mobile computing scenarios

Districting Problems - New Geometrically Motivated Approaches

This thesis focuses on districting problems were the basic areas are represented by points or lines. In the context of points, it presents approaches that utilize the problem\u27s underlying geometrical information. For lines it introduces an algorithm combining features of geometric approaches, tabu search, and adaptive randomized neighborhood search that includes the routing distances explicitly. Moreover, this thesis summarizes, compares and enhances existing compactness measures

FGPGA: An Efficient Genetic Approach for Producing Feasible Graph Partitions

Graph partitioning, a well studied problem of parallel computing has many applications in diversified fields such as distributed computing, social network analysis, data mining and many other domains. In this paper, we introduce FGPGA, an efficient genetic approach for producing feasible graph partitions. Our method takes into account the heterogeneity and capacity constraints of the partitions to ensure balanced partitioning. Such approach has various applications in mobile cloud computing that include feasible deployment of software applications on the more resourceful infrastructure in the cloud instead of mobile hand set. Our proposed approach is light weight and hence suitable for use in cloud architecture. We ensure feasibility of the partitions generated by not allowing over-sized partitions to be generated during the initialization and search. Our proposed method tested on standard benchmark datasets significantly outperforms the state-of-the-art methods in terms of quality of partitions and feasibility of the solutions.Comment: Accepted in the 1st International Conference on Networking Systems and Security 2015 (NSysS 2015

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions