旅行修理工和快速送货工问题的近似算法
Approximation Algorithms for the Traveling Repairman and Speeding Deliveryman Problems
摘要：
针对带时间窗的旅行商问题的两种变形，给出了常数因子多项式时间近似算法。在第一个变体中，旅行修理工问题，目标是找到一个在其时间窗口内访问最大可能数量的位置的旅行。在第二个变体中，加速送货员问题，目标是找到一个使用最小可能加速的旅行，在他们的时间窗口内访问所有位置。对于这两种变体，时间窗口具有单位长度，并且距离度量基于加权的无向图。当输入定义在树而不是一般图上时，给出了具有改进的近似比的算法。该算法还扩展到处理时间窗口的长度落在任何有界范围内。
英文摘要：
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits the maximum possible number of locations during their time windows. In the second variation, the speeding deliveryman problem, the goal is to find a tour that uses the minimum possible speedup to visit all locations during their time windows. For both variations, the time windows are of unit length, and the distance metric is based on a weighted, undirected graph. Algorithms with improved approximation ratios are given for the case when the input is defined on a tree rather than a general graph. The algorithms are also extended to handle time windows whose lengths fall in any bounded range.
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