Pure Strategy Asymmetric Rendezvous on the Line with an Unknown Initial Distance
Steve Alpern, Anatole Beck · Operations Research · 2000
Suppose two blind agents with unit speed are placed a distance H apart on an infinite line, and faced in random directions. Their initial distance H is picked from a distribution F with finite mean μ. We present a pair of rendezvous strategies which do not depend on the distribution F and ensure a meeting in expected time less than 5:514μ. This improves the bound of 5:74μ given by Baston and Gal. Furthermore, the bound we give is best possible for strategies of our type.