Casting Light on the Hidden Bilevel Combinatorial Structure of the Capacitated Vertex Separator Problem

Exploiting Bilevel Optimization Techniques to Disconnect Graphs into Small Components In order to limit the spread of possible viral attacks in a communication or social network, it is necessary to identify critical nodes, the protection of which disconnects the remaining unprotected graph into a bounded number of shores (subsets of vertices) of limited cardinality. In the article “'Casting Light on the Hidden Bilevel Combinatorial Structure of the Capacitated Vertex Separator Problem”, Furini, Ljubic, Malaguti, and Paronuzzi provide a new bilevel interpretation of the associated capacitated vertex separator problem and model it as a two-player Stackelberg game in which the leader interdicts (protects) the vertices, and the follower solves a combinatorial optimization problem on the resulting graph. Thanks to this bilevel interpretation, the authors derive different families of strengthening inequalities and show that they can be separated in polynomial time. The ideas exploited in their framework can also be extended to other vertex/edge deletion/insertion problems or graph partitioning problems by modeling them as two-player Stackelberg games to be solved through bilevel optimization.

Solving Clique Partitioning Problems: A Comparison of Models and Commercial Solvers

Finding good solutions to clique partitioning problems remains a computational challenge. With rare exceptions, finding optimal solutions for all but small instances is not practically possible. However, choosing the most appropriate modeling structure can have a huge impact on what is practical to obtain from exact solvers within a reasonable amount of run time. Commercial solvers have improved tremendously in recent years and the combination of the right solver and the right model can significantly increase our ability to compute acceptable solutions to modest-sized problems with solvers like CPLEX, GUROBI and XPRESS. In this paper, we explore and compare the use of three commercial solvers on modest sized test problems for clique partitioning. For each problem instance, a conventional linear model from the literature and a relatively new quadratic model are compared. Extensive computational experience indicates that the quadratic model outperforms the classic linear model as problem size grows.

Shortest Path Method for Hardware/Software Partitioning Problems

Smart systems are becoming more present in every aspect of our daily lives. The main component of such systems is an embedded system; this latter assures the collection, the treatment, and the transmission of the accurate information in the right time and for the right component. Modern embedded systems are facing several challenges; the objective is to design a system with high performance and to decrease the cost and the development time. Consequently, some robust methodologies like the Codesign were developed to fulfill those requirements. The most important step of the Codesign is the partitioning of the systems' functionalities between a hardware set and a software set. This article deals with this problem and uses a heuristic approach based on shortest path optimizations to solve the problem. The aim is to minimize the total hardware area and to respect a constraint on the overall execution time of the system. Experiments results demonstrate that the proposed method is very fast and gives better results compared to the genetic algorithm.

Stacked Community Prediction: A Distributed Stacking-Based Community Extraction Methodology for Large Scale Social Networks

Nowadays, due to the extensive use of information networks in a broad range of fields, e.g., bio-informatics, sociology, digital marketing, computer science, etc., graph theory applications have attracted significant scientific interest. Due to its apparent abstraction, community detection has become one of the most thoroughly studied graph partitioning problems. However, the existing algorithms principally propose iterative solutions of high polynomial order that repetitively require exhaustive analysis. These methods can undoubtedly be considered resource-wise overdemanding, unscalable, and inapplicable in big data graphs, such as today’s social networks. In this article, a novel, near-linear, and highly scalable community prediction methodology is introduced. Specifically, using a distributed, stacking-based model, which is built on plain network topology characteristics of bootstrap sampled subgraphs, the underlined community hierarchy of any given social network is efficiently extracted in spite of its size and density. The effectiveness of the proposed methodology has diligently been examined on numerous real-life social networks and proven superior to various similar approaches in terms of performance, stability, and accuracy.

ANALYSIS THE CLUSTER PERFORMANCE OF REAL DATASET USING SPSS TOOL WITH K-MEANS APPROACH VIA PCA

Partitioning problems are handled by the idea of cluster and this technique which plays the essential work in mining of data from the given dataset. The K-Means cluster is well accepted theory to apply on huge datasets, but has some drawbacks. The factual dataset is taken from the repository of data used for clustering. Furthermore, as getting the outcome of this procedure is essential to resolve the limitations and quality enhanced of cluster by apply the Principal Component Analysis (PCA) on the dataset. In paper we have demonstrate the results by experimental for factual datasets with dissimilarities. We have worked to validate the experimental significant for the clusters metric and component size minimized for different dataset during the processing on SPSS tool on the basis of eigenvalues. In this research paper we also discussed the comparative analysis of distance between initial centroid of wine and disease of heart dataset at the level of cluster k=2 and k=3.