Abstract
Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower ideals. In this paper, we describe a general-purpose method for finding obstructions by using a bounded treewidth (or pathwidth) search. We illustrate this approach by characterizing certain families of cycle-cover graphs based on the two well-known problems: k-Feedback Vertex Set and k-Feedback Edge Set. Our search is based on a number of algorithmic strategies by which large constants can be mitigated, including a randomized strategy for obtaining proofs of minimality.
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© 1995 Springer-Verlag Berlin Heidelberg
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Cattell, K., Dinneen, M.J., Fellows, M.R. (1995). Obstructions to within a few vertices or edges of acyclic. In: Akl, S.G., Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1995. Lecture Notes in Computer Science, vol 955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60220-8_81
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DOI: https://doi.org/10.1007/3-540-60220-8_81
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