Enumerating Spanning and Connected Subsets in Graphs and Matroids

We show that enumerating all minimal spanning and connected subsets of a given matroid is quasi-polynomially equivalent to the well-known hypergraph transversal problem, and thus 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.

• Type: Conference
• Year: 2006
• Where: ESA
• Authors: Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled M. Elbassioni, Vladimir Gurvich, Kazuhisa Makino
• Keywords: Algorithms, ESA 2006, Incremental Polynomial Time, Incremental Quasi-polynomial Time, Well-known Hypergraph Transversal