eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-07-04
52:1
52:14
10.4230/LIPIcs.ICALP.2018.52
article
A Sublinear Tester for Outerplanarity (and Other Forbidden Minors) With One-Sided Error
Fichtenberger, Hendrik
1
https://orcid.org/0000-0003-3246-5323
Levi, Reut
2
https://orcid.org/0000-0003-3167-1766
Vasudev, Yadu
3
https://orcid.org/0000-0001-7918-7194
Wötzel, Maximilian
4
https://orcid.org/0000-0001-7591-0998
TU Dortmund, Dortmund, Germany
Weizmann Institute of Science, Rehovot, Israel
Indian Institute of Technology Madras, Chennai, India
BGSMath and UPC Barcelona, Barcelona, Spain
We consider one-sided error property testing of F-minor freeness in bounded-degree graphs for any finite family of graphs F that contains a minor of K_{2,k}, the k-circus graph, or the (k x 2)-grid for any k in N. This includes, for instance, testing whether a graph is outerplanar or a cactus graph. The query complexity of our algorithm in terms of the number of vertices in the graph, n, is O~(n^{2/3} / epsilon^5). Czumaj et al. (2014) showed that cycle-freeness and C_k-minor freeness can be tested with query complexity O~(sqrt{n}) by using random walks, and that testing H-minor freeness for any H that contains a cycles requires Omega(sqrt{n}) queries. In contrast to these results, we analyze the structure of the graph and show that either we can find a subgraph of sublinear size that includes the forbidden minor H, or we can find a pair of disjoint subsets of vertices whose edge-cut is large, which induces an H-minor.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol107-icalp2018/LIPIcs.ICALP.2018.52/LIPIcs.ICALP.2018.52.pdf
graph property testing
minor-free graphs