Knowledge Discovery in Graphs Through Vertex Separation

This paper presents our ongoing work on the Vertex Separator Problem (VSP), and its application to knowledge discovery in graphs representing real data. The classic VSP is modeled as an integer linear program. We propose several variants to adapt this model to graphs with various properties. To evaluate the relevance of our approach on real data, we created two graphs of different size from the IMDb database. The model was applied to the separation of these graphs. The results demonstrate how the model is able to semantically separate graphs into clusters.

[1]  Arkady Kanevsky,et al.  Finding all minimum-size separating vertex sets in a graph , 1993, Networks.

[2]  Curt Jones,et al.  Finding Good Approximate Vertex and Edge Partitions is NP-Hard , 1992, Inf. Process. Lett..

[3]  Jeffrey D Ullma.  Computational Aspects of VLSI , 1984 .

[4]  Egon Balas,et al.  The vertex separator problem: a polyhedral investigation , 2005, Math. Program..

[5]  Nicholas Hopper,et al.  Routing around decoys , 2012, CCS.

[6]  Bin Fu,et al.  Multi-Directional Width-Bounded Geometric Separator and protein Folding , 2008, Int. J. Comput. Geom. Appl..

[7]  Charu C. Aggarwal,et al.  Graph Clustering , 2010, Encyclopedia of Machine Learning and Data Mining.

[8]  Timothy A. Davis,et al.  Direct methods for sparse linear systems , 2006, Fundamentals of algorithms.

[9]  William W. Hager,et al.  Continuous quadratic programming formulations of optimization problems on graphs , 2015, Eur. J. Oper. Res..

[10]  Jin-Kao Hao,et al.  Breakout local search for the quadratic assignment problem , 2013, Appl. Math. Comput..

[11]  Marie-Jean Meurs,et al.  An exact algorithm for solving the vertex separator problem , 2011, J. Glob. Optim..

[12]  R. Tarjan,et al.  A Separator Theorem for Planar Graphs , 1977 .

[13]  Egon Balas,et al.  The vertex separator problem: algorithms and computations , 2005, Math. Program..

[14]  Jin-Kao Hao,et al.  Breakout Local Search for the Vertex Separator Problem , 2013, IJCAI.

[15]  Satu Elisa Schaeffer,et al.  Graph Clustering , 2017, Encyclopedia of Machine Learning and Data Mining.

[16]  Junichiro Fukuyama,et al.  NP-completeness of the Planar Separator Problems , 2006, J. Graph Algorithms Appl..