Fence patrolling by mobile agents with distinct speeds
This addresses a theoretical problem in robotics and distributed systems for researchers, but it is incremental as it refines an existing conjecture.
The paper tackled the problem of patrolling a fence with mobile agents of distinct speeds, disproving a conjecture by Czyzowicz et al. that the maximum fence length is (v_1 + ... + v_k)/2, using a counterexample with k=6 agents, and confirmed it holds for k=2,3.
Suppose we want to patrol a fence (line segment) using k mobile agents with given speeds v_1, ..., v_k so that every point on the fence is visited by an agent at least once in every unit time period. Czyzowicz et al. conjectured that the maximum length of the fence that can be patrolled is (v_1 + ... + v_k)/2, which is achieved by the simple strategy where each agent i moves back and forth in a segment of length v_i/2. We disprove this conjecture by a counterexample involving k = 6 agents. We also show that the conjecture is true for k = 2, 3.