A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A sublinear bipartiteness tester for bounded degree graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Shallow excluded minors and improved graph decompositions
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Approximating the Minimum Spanning Tree Weight in Sublinear Time
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Short paths in expander graphs
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Testing Expansion in Bounded-Degree Graphs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Every minor-closed property of sparse graphs is testable
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Property Testing on k-Vertex-Connectivity of Graphs
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Local Graph Partitions for Approximation and Testing
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
An efficient partitioning oracle for bounded-treewidth graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
A quasi-polynomial time partition oracle for graphs with an excluded minor
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We present an efficient algorithm for testing outerplanarity of graphs in the bounded degree model. In this model, given a graph G with n vertices and degree bound d, we should distinguish with high probability the case that G is outerplanar from the case that modifying at least an ε-fraction of the edge set of G is necessary to make G outerplanar. Our algorithm runs in Õ(1/ε13 d6 + d/ε2) time, which is independent of the size of graphs. This is the first algorithm for a non-trivial minorclosed property whose time complexity is polynomial in 1/ε and d. To achieve the time complexity, we exploit the tree-like structure inherent to an outerplanar graph using the microtree/macrotree decomposition of a tree. As a corollary, we also show an algorithm that tests whether a given graph is a cactus with time complexity Õ(1/ε13 d6 + d/ε2).