Improved algorithm for permutation testing
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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, <cit.> propose a non-adaptive algorithm with query complexity (log n)^O(k^2). <cit.> then improve the query complexity of non-adaptive algorithm to Ω((log n)^⌊log k⌋). Further, <cit.> 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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