  Motif finding is an important step for the detection of rare events occurring
in a set of DNA or protein sequences. Extraction of information about these
rare events can lead to new biological discoveries. Motifs are some important
patterns that have numerous applications including the identification of
transcription factors and their binding sites, composite regulatory patterns,
similarity between families of proteins, etc. Although several flavors of motif
searching algorithms have been studied in the literature, we study the version
known as $ (l, d) $-motif search or Planted Motif Search (PMS). In PMS, given
two integers $ l $, $ d $ and $ n $ input sequences we try to find all the
patterns of length $ l $ that appear in each of the $ n $ input sequences with
at most $ d $ mismatches. We also discuss the quorum version of PMS in our work
that finds motifs that are not planted in all the input sequences but at least
in $ q $ of the sequences. Our algorithm is mainly based on the algorithms
qPMSPrune, qPMS7, TraverStringRef and PMS8. We introduce some techniques to
compress the input strings and make faster comparison between strings with
bitwise operations. Our algorithm performs a little better than the existing
exact algorithms to solve the qPMS problem in DNA sequence. We have also
proposed an idea for parallel implementation of our algorithm.
