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Complaint no affidavit been helping people love boost probabilities talks pushed on the stack. For example, at the point where the chain at locations 2 and 4 is sorted, the positions at 3 and 5 have already been ranked Thus, we already know from those ranks that position 5 must come first. This optimization is known as induced sorting. This optimization is insufficient to prevent worst case O behavior on data with high average LCP. To handle this, MSufSort v2 detects repeating strings and applies the observation that if the suffix order of the last repeat is known, then the same order can be applied to all of the remaining prefixes and they can be written into the Once those ranks are applied, other rotations of the repeating string are ranked by induced sorting. Itoh-Tanaka. The open source dark compressor by Dmitry Malyshev uses Itoh-Tanaka suffix array sorting for the forward BWT transform. Itoh-Tanaka has O worst case complexity, additional steps such as LZP preprocessing are needed to avoid common prefixes. Itoh-Tanaka classifies each input byte by whether or not it is larger than the byte following it. For example: 0 2 4 6 Input: B A N A N A Type: L S L S L L S We denote a character as type L if it is lexicographically larger than the byte after it and S if it is smaller or equal. Itoh-Tanaka sorts the S characters using ordinary string comparison, then induces the sort order of the L bytes a single pass. The first step is to put the unsorted type S characters into the suffix array, SA. We note that SA has 256 buckets plus the terminating sentinel, and furthermore each bucket is divided into two parts with all of the L bytes on the left and S on the right. Thus: SA: A= B= N= Next we sort the right halves of all of the buckets that have two or more type S symbols. Itoh and Tanaka use a multikey quicksort although any string sorting algorithm could be used. Recall that the quicksort algorithm picks one element at random, called a pivot, then moves all elements smaller than the pivot to the left side of the array and all others to the right side, with the pivot between. Then it recursively quicksorts the two halves. a multikey quicksort, the array is divided into three parts based on the first character of the string. The left and right parts are recursively sorted, and the middle part is recursively sorted using the next character of the string as the sort key, similar to a radix sort. After sorting we have: SA: A= B= N= We now have enough information SA to induce the rest of the elements. We can use the fact that when the order of two suffixes SA is known and they are both preceded by the same character, then those two longer suffixes must also be the same order. For example, if we know that suffix 6 comes before 4 and both are preceded by A, then it must be the case that suffix 5 comes before 3 The procedure for the induced sort is to scan SA left to right. For each pointer already filled we look at the character to its left. If it is type L then we place it the leftmost available position the appropriate bucket. For example: SA: A= B= N= Scan 6. Input 'A' is type L, we put 5 bucket A. SA: A= B= N= Scan 5. Input 'N' is type L, we put 4 at the left of bucket N. SA: A= B= N= Scan 3. Input 'N' is type L, we put 2 at the next open