The Beachcombers' Problem：Walking and Searching with Mobile Robots（海滩流浪者问题：移动机器人的行走和搜索）
The Beachcombers' Problem: Walking and Searching with Mobile Robots
摘要：
我们介绍和研究一个新的问题，关于探索的几何域的移动机器人。考虑一条线段$[0,I]$和一组放置在其端点之一的$n$移动机器人$r_1,r_2,..., r_n$。每个机器人具有{ \em搜索速度} $s_i$和{ \em行走速度} $w_i$，其中$s_i <w_i$。我们假设每个机器人都知道集合中的机器人数量及其相应的速度。在每个时刻，机器人$r_i$或者沿着不超过其行走速度$w_i$的段的一部分行走，或者以不超过$s_i$的速度搜索段的一部分。当至少一个$n$机器人已经搜索了段$[0,I]$的每个点时，完成对段的搜索。我们希望为机器人开发{ \em移动时间表}（算法），以尽可能快地完成对路段的搜索。更确切地说，我们想要最大化移动性调度的{ \em速度}（等于段长度与完成调度的时间的比率）。我们首先分析离线的情况下，当机器人知道的长度段，是要搜索。我们给出了一个算法产生的移动性调度任意的步行和搜索速度，并证明其最优性。然后，我们提出了一个在线算法，当机器人不知道在事先的实际长度段搜索。这种算法的速度$S$被定义为$S = \inf_{I_L} S(I_L)$，其中$S(I_L)$表示段$I_L=[0,L]$的搜索速度。我们证明了所提出的在线算法是2-竞争的。当机器人的步行速度相同时，竞争比更好。
英文摘要：
We introduce and study a new problem concerning the exploration of a geometric domain by mobile robots. Consider a line segment $[0,I]$ and a set of $n$ mobile robots $r_1,r_2,..., r_n$ placed at one of its endpoints. Each robot has a {\em searching speed} $s_i$ and a {\em walking speed} $w_i$, where $s_i <w_i$. We assume that each robot is aware of the number of robots of the collection and their corresponding speeds. At each time moment a robot $r_i$ either walks along a portion of the segment not exceeding its walking speed $w_i$ or searches a portion of the segment with the speed not exceeding $s_i$. A search of segment $[0,I]$ is completed at the time when each of its points have been searched by at least one of the $n$ robots. We want to develop {\em mobility schedules} (algorithms) for the robots which complete the search of the segment as fast as possible. More exactly we want to maximize the {\em speed} of the mobility schedule (equal to the ratio of the segment length versus the time of the completion of the schedule). We analyze first the offline scenario when the robots know the length of the segment that is to be searched. We give an algorithm producing a mobility schedule for arbitrary walking and searching speeds and prove its optimality. Then we propose an online algorithm, when the robots do not know in advance the actual length of the segment to be searched. The speed $S$ of such algorithm is defined as $S = \inf_{I_L} S(I_L)$ where $S(I_L)$ denotes the speed of searching of segment $I_L=[0,L]$. We prove that the proposed online algorithm is 2-competitive. The competitive ratio is shown to be better in the case when the robots' walking speeds are all the same.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
