RENDEZVOUS SEARCH ON THE LINE WITH DISTINGUISHABLE PLAYERS

Two players are placed on the real line at a distance d with a distrib ution F known to both. Neither knows the direction of the other, nor d o they have a common notion of a positive direction on the line. We se ek the least expected rendezvous time R equals R(F) in which they can meet, given maximum speeds of one. We consider the cases where F is a bounded , point, discrete, or finite mean distribution. We obtain uppe r bounds or exact values for R and in one case an optimality condition for search strategies. A connection with Beck's linear search problem is established.