Pure strategy asymmetric rendezvous on the line with an unknown initial distance

Suppose two blind agents with unit speed are placed a distance H apart on a n infinite line, and faced in random directions. Their initial distance H i s picked from a distribution F with finite mean mu. We present a pair of re ndezvous strategies which do not depend on the distribution F and ensure a meeting in expected time less than 5.514 mu. This improves the bound of 5.7 4 mu given by Baston and Gal. Furthermore, the bound we give is best possib le for strategies of our type.