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Every Property of Outerplanar Graphs is Testable

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Jasine Babu, Areej Khoury, and Ilan Newman. Every Property of Outerplanar Graphs is Testable. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2016.21

Abstract

A D-disc around a vertex v of a graph G=(V,E) is the subgraph induced by all vertices of distance at most D from v. We show that the structure of an outerplanar graph on n vertices is determined, up to modification (insertion or deletion) of at most epsilon n edges, by a set of D-discs around the vertices, for D=D(epsilon) that is independent of the size of the graph. Such a result was already known for planar graphs (and any hyperfinite graph class), in the limited case of bounded degree graphs (that is, their maximum degree is bounded by some fixed constant, independent of |V|). We prove this result with no assumption on the degree of the graph. A pure combinatorial consequence of this result is that two outerplanar graphs that share the same local views are close to be isomorphic. We also obtain the following property testing results in the sparse graph model: * graph isomorphism is testable for outerplanar graphs by poly(log n) queries. * every graph property is testable for outerplanar graphs by poly(log n) queries. We note that we can replace outerplanar graphs by a slightly more general family of k-edge-outerplanar graphs. The only previous general testing results, as above, where known for forests (Kusumoto and Yoshida), and for some power-law graphs that are extremely close to be bounded degree hyperfinite (by Ito).
Keywords
• Property testing
• Isomorphism
• Outerplanar graphs

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References

1. Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. A combinatorial characterization of the testable graph properties: It’s all about regularity. SIAM J. Comput., 39(1):143-167, 2009. URL: http://dx.doi.org/10.1137/060667177.
2. Itai Benjamini, Oded Schramm, and Asaf Shapira. Every minor-closed property of sparse graphs is testable. In Proceedings of the 40th Annual ACM Symposium on Theory of Computing, 2008, pages 393-402, 2008. URL: http://dx.doi.org/10.1145/1374376.1374433.
3. Oded Goldreich, Shafi Goldwasser, and Dana Ron. Property testing and its connection to learning and approximation. J. ACM, 45(4):653-750, 1998. URL: http://dx.doi.org/10.1145/285055.285060.
4. Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. Local graph partitions for approximation and testing. In 50th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2009, pages 22-31, 2009. URL: http://dx.doi.org/10.1109/FOCS.2009.77.
5. Hiro Ito. Every property is testable on a natural class of scale-free multigraphs. CoRR, abs/1504.00766, 2015. URL: http://arxiv.org/abs/1504.00766.
6. Mitsuru Kusumoto and Yuichi Yoshida. Testing forest-isomorphism in the adjacency list model. In Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings, Part I, pages 763-774, 2014. URL: http://dx.doi.org/10.1007/978-3-662-43948-7_63.
7. Reut Levi and Dana Ron. A quasi-polynomial time partition oracle for graphs with an excluded minor. ACM Trans. Algorithms, 11(3):24:1-24:13, 2015. URL: http://dx.doi.org/10.1145/2629508.
8. Richard J. Lipton and Robert Endre Tarjan. Applications of a planar separator theorem. SIAM Journal on Computing, 9(3):615-627, 1980.
9. Ilan Newman and Christian Sohler. Every property of hyperfinite graphs is testable. SIAM J. Comput., 42(3):1095-1112, 2013. URL: http://dx.doi.org/10.1137/120890946.
10. Krzysztof Onak. New sublinear methods in the struggle against classical problems. PhD Thesis, Massachusetts Institute of Technology, 2010.
11. Ronitt Rubinfeld and Madhu Sudan. Robust characterizations of polynomials with applications to program testing. SIAM J. Comput., 25(2):252-271, 1996. URL: http://dx.doi.org/10.1137/S0097539793255151.
12. Christian Sohler. Private Communication, 2015.
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