运动修复的近似算法
Approximation Algorithms for Movement Repairmen
摘要：
在{ \em Movement Repairmen（MR）}问题中，我们给出了度量空间$(V, d)$以及分别具有其起始仓库$s_1, s_2, ..., s_k \in V$和速度$v_1, v_2, ..., v_k \geq 0$的$k$修理者$r_1, r_2, ..., r_k$的集合$R$，以及分别具有起始位置$s'_1, s'_2, ..., s'_m \in V$和速度$v'_1, v'_2, ..., v'_m \geq 0$的$m$客户端$c_1, c_2, ..., c_m$的集合$C$。如果$t$是客户端$c_j$与节点$u$处的任何修理工（例如，$r_i$）并置的最早时间，则我们说客户端由$u$处的$r_i$服务，并且其延迟是$t$。在（\smr{}）问题的目标是计划所有的维修人员和客户端的移动，以最小化的总和（平均）的客户端延迟。例如，这个问题的动机来自Amazon Delivery \cite{amazon}和USPS gopost \cite{gopost}。我们给出了\smr{}问题的第一个$O(\log n)$ -近似算法。
英文摘要：
In the {\em Movement Repairmen (MR)} problem we are given a metric space $(V, d)$ along with a set $R$ of $k$ repairmen $r_1, r_2, ..., r_k$ with their start depots $s_1, s_2, ..., s_k \in V$ and speeds $v_1, v_2, ..., v_k \geq 0$ respectively and a set $C$ of $m$ clients $c_1, c_2, ..., c_m$ having start locations $s'_1, s'_2, ..., s'_m \in V$ and speeds $v'_1, v'_2, ..., v'_m \geq 0$ respectively. If $t$ is the earliest time a client $c_j$ is collocated with any repairman (say, $r_i$) at a node $u$, we say that the client is served by $r_i$ at $u$ and that its latency is $t$. The objective in the (\smr{}) problem is to plan the movements for all repairmen and clients to minimize the sum (average) of the clients latencies. The motivation for this problem comes, for example, from Amazon Locker Delivery \cite{amazon} and USPS gopost \cite{gopost}. We give the first $O(\log n)$-approximation algorithm for the \smr{} problem.
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