Breaking Lander-Waterman’s Coverage Bound

Abstract

Lander-Waterman’s coverage bound establishes the total number of reads required to cover the whole genome of size G bases. In fact, their bound is a direct consequence of the well-known solution to the coupon collector’s problem which proves that for such genome, the total number of bases to be sequenced should be O(G ln G). Although the result leads to a tight bound, it is based on a tacit assumption that the set of reads are first collected through a sequencing process and then are processed through a computation process, i.e., there are two different machines: one for sequencing and one for processing. In this paper, we present a significant improvement compared to Lander-Waterman’s result and prove that by combining the sequencing and computing processes, one can re-sequence the whole genome with as low as O(G) sequenced bases in total. Our approach also dramatically reduces the required computational power for the combined process. Simulation results are performed on real genomes with different sequencing error rates. The results support our theory predicting the log G improvement on coverage bound and corresponding reduction in the total number of bases required to be sequenced.