On the Complexity of Determining the Period of a String
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
Theoretical Issues of Cluster Pattern Interfaces
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Optimal discovery of repetitions in 2D
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Constant-Time word-size string matching
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Cycle detection and correction
ACM Transactions on Algorithms (TALG)
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All algorithms below are optimal alphabet-independent parallel CRCW PRAM algorithms. In one dimension: Given a pattern string of length m for the string-matching problem, we design an algorithm that computes a deterministic sample of a sufficiently long substring in constant time. This problem used to be a bottleneck in the pattern preprocessing for one- and two-dimensional pattern matching. The best previous time bound was O(log/sup 2/ m/log log m). We use this algorithm to obtain the following results. 1. Improving the preprocessing of the constant-time text search algorithm from O(log/sup 2/ m/log log m) to n(log log m), which is now best possible. 2. A constant-time deterministic string-matching algorithm in the case that the text length n satisfies n=/spl Omega/(m/sup 1+/spl epsiv//) for a constant /spl epsiv/0. 3. A simple probabilistic string-matching algorithm that has constant time with high probability for random input. 4. A constant expected time Las-Vegas algorithm for computing the period of the pattern and all witnesses and thus string matching itself, solving the main open problem remaining in string matching.