A Note on Cro hemore ' s Repetitions Algorithm a Fast Spa

Abstra t. The spa e requirement of Cro hemore's repetitions algorithm is generally estimated to be about 20MN bytes of memory, where N is the length of the input string and M the number of bytes required to store the integer N . The same algorithm an also be used in other ontexts, for instan e to ompute the suÆx tree of the input string in O(N logN) time for the purpose of data ompression. In su h ontexts the large spa e requirement of the algorithm is a signi ant drawba k. There are of ourse several newer spa e-eÆ ient algorithms with the same time omplexity that an ompute suÆx trees or arrays. However, in a tual implementations, these algorithms may not be faster than Cro hemore's. Therefore, we onsider it interesting enough to des ribe a new approa h based on the same mathemati al prin iples and observations that were put forth in Cro hemore's original paper, but whose spa e requirement is 10MN bytes. Additional advantages of the approa h are the ease with whi h it an be implemented in C/C++ (as we have done) and the apparent speed of su h an implementation in omparison to other implementations of the original algorithm.