Parallel On-Line Searching∗

We consider the problem where p searchers explore m > p half-lines, all joined at a common origin. The searchers travel at unit speed and the goal is to find a single object, or “exit” whose location is bounded away from the origin. We consider two minmax measures of effectiveness for a search strategy. The first is the worst case distancecompetitive ratio. This is the smallest value that exceeds the fraction (total distance covered until discovery)/(distance of exit from origin) for every exit location in the search space. The second is the worst case time-competitive ratio. This is the smallest value that exceeds the fraction (time until discovery)/(distance of exit from origin) for every exit location in the search space. Note that the denominator of this competitive ratio coincides with the amount of time it would take a searcher with perfect knowledge to reach the exit. In this paper we propose optimal deterministic on-line strategies for solving these problems.