Parallel Searching on m Rays

In this paper we investigate parallel searching on m concurrent rays. We assume that a target t is located somewhere on one of the rays and that a group of m point robots has to reach t. Furthermore, we assume that the robots have no way of communicating over distance. Given a strategy S we are interested in the competitive ratio which is deened as the ratio of the time needed by the robots using S and the time needed if the location of t is known in advance. If a lower bound on the distance to the target is known, then there is a simple strategy which achieves a competitive ratio of 9 | independent of m. We show that even in the case m = 2 there is a lower bound of 9 on the competitive ratio for two large classes of strategies. Moreover, we show that a lower bound of 9 for m = 2 implies a lower bound of 9 for m > 2 | as is to be expected. If the minimum distance to the target is not known in advance, then we show a lower bound on the competitive ratio of 1 + 2(k + 1) k+1 =k k where k = dlog me. We also present a strategy that achieves this competitive ratio.