Abstract
Given graphs G and H, we propose a method to implicitly enumerate topological-minor-embeddings of H in G using decision diagrams. We show a useful application of our method to enumerating subgraphs characterized by forbidden topological minors, that is, planar, outerplanar, series-parallel, and cactus subgraphs. Computational experiments show that our method can find all planar subgraphs in a given graph at most five orders of magnitude faster than a naive backtracking-based method.
This work was supported by JSPS KAKENHI Grant Numbers JP15H05711, JP18H04091, JP18K04610, JP18K11153, and JP19J21000.
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Notes
- 1.
In another definition, F is homeomorphic to H if some subdivision of F is isomorphic to some subdivision of H. However, we allow subdividing only for H because H is “contracted enough” when it is a forbidden topological minor, that is, H does not contain redundant vertices with degree 2.
- 2.
To avoid confusion, we use the terms “node” and “arc” for a \((c+1)\)-DD and use “vertex” and “edge” for an input graph.
- 3.
- 4.
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Nakahata, Y., Kawahara, J., Horiyama, T., Minato, Si. (2020). Implicit Enumeration of Topological-Minor-Embeddings and Its Application to Planar Subgraph Enumeration. In: Rahman, M., Sadakane, K., Sung, WK. (eds) WALCOM: Algorithms and Computation. WALCOM 2020. Lecture Notes in Computer Science(), vol 12049. Springer, Cham. https://doi.org/10.1007/978-3-030-39881-1_18
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