An algorithm for the modular decomposition of hypergraphs Paola Bonizzoni and Gianluca Della Vedova Dipartimento di Scienze dell’Informazione Universit`a Degli Studi di Milano Via Comelico 39/41, 20135 Milano – ITALY e-mail {bonizzon,dellaved}@dsi.unimi.it Abstract We propose an O(n 4 ) algorithm to build the modu- lar decomposition tree of hypergraphs of dimension 3 and show how this algorithm can be generalized to compute in O(n 3k−5 ) time the decomposition of hy- pergraphs of any fixed dimension k. c  1999 by Academic Press. This material has been published in Journal of Algorithms 32(2), pp. 65 − 85, 1999, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Academic Press. This material may not be copied or reposted without explicit permission. This paper is available on IDEAL, http://www.idealibrary.com Preliminary version of this paper appeared in “Proceedings of the 21 st Workshop on Graph-Theoretic Concepts in Computer Science,” Lecture Notes in Computer Science, Vol. 1017, pp. 303-317, Springer-Verlag, Berlin/New York, 1995 1