Consider n identical relocatable sensors, with sensing range r and visibility range 2r, initially placed at arbitrary positions on a line segment barrier; each sensor can detect the presence of an intruder in its sensing range, and is said to cover the portion of the barrier that intersects with its sensing range. Sensors operate in Look-Compute-Move cycles: in a cycle a sensor determines the positions of sensors in its visibility range, it computes its next position (within its visibility range), and then moves to the calculated position. The barrier coverage problem we consider is for the sensors to independently make decisions and movements so to reach final positions whereby they collectively cover the barrier; in particular we are interested in oblivious (or memoryless) sensors, and focus on the impact that the level of synchrony and the presence/absence of orientation (i.e., global notion of “left-right”) have on the solvability of the problem.

It is known that without orientation, oblivious sensors can solve the problem if they are fully synchronous (i.e., they operate in synchronous rounds and are all active at every round). In this paper, we prove that orientation is critical to being able to solve the problem if we relax the assumption of full synchronization.

We first show that if sensors are unoriented, then barrier coverage is unsolvable even in the semi-synchronous setting. In contrast, if sensors agree on a global orientation, then we give an algorithm for barrier coverage, even in the completely asynchronous setting. Finally, we extend the existing result of Cohen and Peleg and show that convergence to barrier coverage by unoriented sensors in the semi-synchronous model is possible with bounded visibility range $2r+\rho$ (for arbitrarily small $\rho >0$) and bounded mobility range r.

考虑n 个相同的可重定位传感器，其感应范围为r，可见范围为 2 r，最初放置在线段屏障上的任意位置；每个传感器都可以在其感应范围内检测到入侵者的存在，并且据说可以覆盖与其感应范围相交的屏障部分。传感器以 Look-Compute-Move 循环运行：在一个循环中，传感器确定传感器在其可见范围内的位置，计算其下一个位置（在其可见范围内），然后移动到计算出的位置。该栅栏覆盖我们考虑的问题是传感器独立做出决定和移动，以便到达最终位置，从而共同覆盖障碍物；特别是我们对遗忘（或无记忆）传感器感兴趣，并关注同步水平和方向的存在/不存在（即“左右”的全局概念）对问题可解性的影响。

众所周知，在没有定向的情况下，不经意传感器如果完全同步（即，它们在同步轮次中运行并且在每一轮中都处于活动状态）可以解决问题。在本文中，我们证明如果我们放宽完全同步的假设，方向对于解决问题至关重要。

我们首先表明，如果传感器是无方向的，那么即使在半同步设置中，障碍覆盖也是无法解决的。相比之下，如果传感器就全局方向达成一致，那么即使在完全异步的设置中，我们也会给出屏障覆盖的算法。最后，我们扩展了 Cohen 和 Peleg 的现有结果，并表明在可见范围有限的情况下，半同步模型中无定向传感器收敛到障碍覆盖是可能的$2r+\rho$ （对于任意小 $\rho >0$) 和有界移动范围r。