  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.
