Suppose we want to patrol a fence (line segment) using $$k$$k mobile agents with given speeds $$v _1$$v1,.., $$v _k$$vk 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 $$(v _1 + \cdots + v _k)/2$$(v1+⋯+vk)/2, which is achieved by the simple strategy where each agent $$i$$i moves back and forth in a segment of length $$v _i / 2$$vi/2. We disprove this conjecture by a counterexample involving $$k = 6$$k=6 agents. We also show that the conjecture is true for $$k \le 3$$k≤3.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Hardware and Architecture
- Computer Networks and Communications
- Computational Theory and Mathematics