Seed optimization for i.i.d. similarities is no easier than optimal Golomb ruler design

The spaced seed is a filtration method to efficiently identify the regions of interest in string similarity searches. It is important to find the optimal spaced seed that achieves the highest search sensitivity. For some simple distributions of the similarities, the seed optimization problem was proved to be not NP-hard. On the other hand, no polynomial time algorithm has been found despite the extensive researches in the literature. In this article we examine the hardness of the seed optimization problem by a polynomial time reduction from the optimal Golomb ruler design problem, which is a well-known difficult (but not NP-hard) problem in combinatorial design.