A new hash function and its use in read mapping on genome

Mapping reads onto genomes is an indispensable step in sequencing data analysis. A widely used method to speed up mapping is to index a genome by a hash table, in which genomic positions of $k$-mers are stored in the table. The hash table size increases exponentially with the $k$-mer length and thus the traditional hash function is not appropriate for a $k$-mer as long as a read. We present a hashing mechanism by two functions named $score1$ and $score2$ which can hash sequences with the length of reads. The size of hash table is directly proportional to the genome size, which is absolutely lower than that of hash table built by the conventional hash function. We evaluate our hashing system by developing a read mapper and running the mapper on $E. coli$ genome with some simulated data sets. The results show that the high percentage of simulated reads can be mapped to correct locations on the genome.