Faster exact distributions of pattern statistics through sequential elimination of states

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• 作者：Donald E. K. Martin ; Laurent Noé
• 关键词：Active proper suffix ; Auxiliary Markov chain ; Computational efficiency ; Extended seed patterns ; Minimal deterministic finite automaton ; Overlapping pattern occurrences ; Seeded alignments ; Spaced seed coverage
• 刊名：Annals of the Institute of Statistical Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：69
• 期：1
• 页码：231-248
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance;
• 出版者：Springer Japan
• ISSN：1572-9052
• 卷排序：69

文摘

When using an auxiliary Markov chain (AMC) to compute sampling distributions, the computational complexity is directly related to the number of Markov chain states. For certain complex pattern statistics, minimal deterministic finite automata (DFA) have been used to facilitate efficient computation by reducing the number of AMC states. For example, when statistics of overlapping pattern occurrences are counted differently than non-overlapping occurrences, a DFA consisting of prefixes of patterns extended to overlapping occurrences has been generated and then minimized to form an AMC. However, there are situations where forming such a DFA is computationally expensive, e.g., with computing the distribution of spaced seed coverage. In dealing with this problem, we develop a method to obtain a small set of states during the state generation process without forming a DFA, and show that a huge reduction in the size of the AMC can be attained.