The online $k$-taxi problem, introduced in 1990 by Fiat, Rabani and Ravid, is a generalization of the $k$-server problem where $k$ taxis must serve a sequence of requests in a metric space. Each request is a pair of two points, representing the pick-up and drop-off location of a passenger. In the interesting ''hard'' version of the problem, the cost is the total distance that the taxis travel without a passenger. The problem is known to be substantially harder than the $k$-server problem, and prior to this work even for $k=3$ taxis it has been unknown whether a finite competitive ratio is achievable on general metric spaces. We present an $O(1)$-competitive algorithm for the $3$-taxi problem.

翻译：在线$k$出租车问题由Fiat、Rabani和Ravid于1990年提出，是$k$服务器问题在度量空间中的推广，其中$k$辆出租车需服务一系列请求。每个请求由两个点组成，分别表示乘客的上车地点和下车地点。在该问题有趣的“困难”版本中，成本定义为出租车在无乘客状态下行驶的总距离。已知该问题比$k$服务器问题更为复杂，且在本研究之前，即使对于$k=3$辆出租车的情况，在一般度量空间上是否可实现有限竞争比仍属未知。我们提出了一种针对3出租车问题的$O(1)$竞争算法。