Superiority and Complexity of the Spaced Seeds

Optimal spaced seeds were introduced by the theoretical computer science community to bioinformatics to effectively increase homology search sensitivity. They are now serving thousands of homology search queries daily. While dozens of papers have been published on optimal spaced seeds since their invention, many fundamental questions still remain unanswered. In this paper, we settle several open questions in this area. Specifically, we prove that when the length of a non-uniformly spaced seed is bounded by an exponential function of the seed weight, the seed outperforms strictly the traditional consecutive seed in both (i) the average number of non-overlapping hits and (ii) the asymptotic hit probability. Then, we study the computation of the hit probability of a spaced seed, solving three more open questions: (iii) hit probability computation in a uniform homologous region is NP-hard and (iv) it admits a PTAS; (v) the asymptotic hit probability is computable in exponential time in seed length, independent of the homologous region length.