On-line parallel heuristics, processor scheduling and robot searching under the competitive framework

Abstract

In this paper we investigate parallel searches on m concurrent rays for a point target t located at some unknown distance along one of the rays. A group of p agents or robots moving at unit speed searches for t. The search succeeds when an agent reaches the point t. Given a strategy S the competitive ratio is the ratio of the time needed by the agents to find t using S and the time needed if the location of t had been known in advance. We provide a strategy with competitive ratio of 1+2( m/ p−1)( m/( m− p)) m/ p and prove that this is optimal. This problem has applications in multiple heuristic searches in AI as well as robot motion planning. The case p = 1 is known in the literature as the cow path problem.