Fast phased small RNA cycle counting algorithms

Counting phased small RNA cycles (PSRC) from mapped small RNA positions is a repeatedly invoked subproblem in the computation of identifying TRANS-ACTING siRNA (TAS) loci and loci of other small RNAs forming through mechanisms similar to that of transacting small interfering RNAs (ta-siRNAs). The efficiency of counting PSRC has a clear impact on the efficiency of the algorithms predicting these loci. There are two closely related variants on counting PSRC in real applications: WPSRC, which counts the number of distinct small RNAs falling onto the phased positions in a sliding window, and MPSRC, which counts the maximum consecutive PSRC from mapped small RNA positions. In this paper, we develop fast algorithms for both WPSRC and MPSRC. Our algorithms have O(max(S)) time complexity, while the existing algorithm and its variant have O(|S|·max(S)) and O(|S|·L) time complexity for MPSRC and WPSRC respectively, where S is a set of mapped small RNA positions and L the length of sliding windo