A new algorithm for Golomb ruler derivation and proof of the 19 mark ruler

A new parallel distributed algorithm for Golomb (1977) ruler derivation is presented. This algorithm was used to prove computationally the optimality of three rulers. Two of these were previously proven but yet unpublished, and the authors' independent derivation confirmed these results. The last ruler, of 19 marks and size 246, was known to be near-optimal and was computationally proven optimal in this work.