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An Algorithm for the Modular Decomposition of Hypergraphs

✍ Scribed by Paola Bonizzoni; Gianluca Della Vedova


Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
147 KB
Volume
32
Category
Article
ISSN
0196-6774

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✦ Synopsis


We propose an O n algorithm to build the modular decomposition tree of hypergraphs of dimension three and show how this algorithm can be generalized to

time the decomposition of hypergraphs of any fixed dimension k.


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A module of an undirected graph G = V E is a set X of vertices that have the same set of neighbors in V \X. The modular decomposition is a unique decomposition of the vertices into nested modules. We give a practical algorithm with an O n + mΞ± m n time bound and a variant with a linear time bound.

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## Abstract Chung (F. R. K. Chung, On the decomposition of graphs, __SIAM J. Algebraic Discrete Methods__ 23 (1981), 1–12.) and independently GyΓΆri and Kostochka (E. GyΓΆri and A. V. Kostochka, On a problem of G. O. H. Katona and T. TarjΓ‘n, __Acta Math. Acad. Sci. Hung.__ 34 (1979), 321–327.) proved

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## Abstract In this work a methodology is presented for the rigorous optimization of nonlinear programming problems in which the objective function and (or) some constraints are represented by noisy implicit black box functions. The special application considered is the optimization of modular proc