We study the problem of testing forbidden patterns. The patterns that are of significant interest include monotone pattern and (1,3,2)-pattern. For the problem of testing monotone patterns, newman2019testing propose a non-adaptive algorithm with query complexity (\log n)^{O(k^2)}. ben2019finding then improve the query complexity of non-adaptive algorithm to \Omega((\log n)^{\lfloor\log k\rfloor}). Further, ben2019optimal propose an adaptive algorithm for testing monotone pattern with optimal sample complexity O(\log n). However, the adaptive algorithm and the analysis are rather complicated. In this paper, we provide a simple adaptive algorithm with one-sided error for testing monotone permutation. We also present an algorithm with improved query complexity for testing (1,3,2) pattern .
We study the problem of testing forbidden patterns. The patterns that are of significant interest include monotone pattern and (1,3,2)-pattern. For the problem of testing monotone patterns, newman2019testing propose a non-adaptive algorithm with query complexity (\log n)^{O(k^2)}. ben2019finding then improve the query complexity of non-adaptive algorithm to \Omega((\log n)^{\lfloor\log k\rfloor}). Further, ben2019optimal propose an adaptive algorithm for testing monotone pattern with optimal query complexity O(\log n). However, the adaptive algorithm and the analysis are rather complicated. We provide a simple adaptive algorithm with one-sided error for testing monotone permutation. We also present an algorithm with improved query complexity for testing (1,3,2) -pattern .
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