Enumerating spanning and connected subsets in graphs and matroids

Authors:
L. Khachiyan;E. Boros;K. Borys;K. Elbassioni;V. Gurvich;K. Makino
Affiliations:
Department of Computer Science, Rutgers University, Piscataway, NJ;RUTCOR, Rutgers University, Piscataway, NJ;RUTCOR, Rutgers University, Piscataway, NJ;Max-Planck-Institut für Informatik, Saarbrücken, Germany;RUTCOR, Rutgers University, Piscataway, NJ;Division of Mathematical Science for Social Systems, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan
Venue:
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Year:
2006

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Abstract

We show that enumerating all minimal spanning and connected subsets of a given matroid can be solved in incremental quasi-polynomial time. In the special case of graphical matroids, we improve this complexity bound by showing that all minimal 2-vertex connected edge subsets of a given graph can be generated in incremental polynomial time.