Parallel searching on m rays

Abstract

We investigate parallel searching on m concurrent rays. We assume that a target t is located somewhere on one of the rays; we are given a group of m point robots each of which 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 defined as the ratio of the time needed by the robots to reach t using S and the time needed to reach t 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 9 is a lower bound on the competitive ratio for two large classes of strategies if m ≥ 2. If the minimum distance to the target is not known in advance, we show a lower bound on the competitive ratio of 1 + 2(k + 1)k+1=kk where k = [logm]. We also give a strategy that obtains this ratio.