Applications of Hypergraph Theory: A Brief Overview

Like in most fruitful mathematical theories, the theory of hypergraphs has many applications. Hypergraphs model many practical problems in many different sciences. it makes very little time (20 years) that the theory of hypergraphs is used to model situations in the applied sciences. We find this theory in psychology, genetics, \(\ldots \) but also in various human activities. Hypergraphs have shown their power as a tool to understand problems in a wide variety of scientific field. Moreover it well known now that hypergraph theory is a very useful tool to resolve optimization problems such as scheduling problems, location problems and so on. This chapter shows some possible uses of hypergraphs in Applied Sciences.

[1]  Alain Bretto,et al.  Introduction to Hypergraph Theory and Its Use in Engineering and Image Processing , 2004 .

[2]  Elena V. Konstantinova,et al.  Application of hypergraph theory in chemistry , 2001, Discret. Math..

[3]  Bruno Crémilleux,et al.  A Data Mining Formalization to Improve Hypergraph Minimal Transversal Computation , 2007, Fundam. Informaticae.

[4]  Bernhard Schölkopf,et al.  Kernel Methods in Computational Biology , 2005 .

[5]  Alain Bretto,et al.  Hypergraph-Based Image Representation , 2005, GbRPR.

[6]  H. Robbins.  A Theorem on Graphs, with an Application to a Problem of Traffic Control , 1939 .

[7]  Steffen Klamt,et al.  Hypergraphs and Cellular Networks , 2009, PLoS Comput. Biol..

[8]  Alain Bretto,et al.  A reductive approach to hypergraph clustering: An application to image segmentation , 2012, Pattern Recognit..

[9]  Shakhar Smorodinsky,et al.  On The Chromatic Number of Geometric Hypergraphs , 2007, SIAM J. Discret. Math..

[10]  Peter F. Stadler,et al.  A Survey on Hypergraph Products , 2012, Mathematics in Computer Science.

[11]  Marcello Pelillo,et al.  A Game-Theoretic Approach to Hypergraph Clustering , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Liang Huang,et al.  Advanced Dynamic Programming in Semiring and Hypergraph Frameworks , 2008, COLING.

[13]  Tamara G. Kolda,et al.  Graph partitioning models for parallel computing , 2000, Parallel Comput..

[14]  Ronald Fagin,et al.  Degrees of acyclicity for hypergraphs and relational database schemes , 1983, JACM.

[15]  Peter J. Slater.  A Characterization of Soft Hypergraphs , 1978, Canadian Mathematical Bulletin.

[16]  Oded Goldreich.  Using the FGLSS-Reduction to Prove Inapproximability Results for Minimum Vertex Cover in Hypergraphs , 2011, Studies in Complexity and Cryptography.