For addressing the One-Dimensional Road side unit Deployment (D1RD) problem, a greedy approximate algorithm named Greedy2P3E was proposed two years ago, and its approximation ratio was proved to be at least 2/3 for the D1RD problem with EQual-radius RSUs (D1RD-EQ problem). Can better or even tight approximations for Greedy2P3E be found? In this paper, approximation ratio of Greedy2P3E is re-inspected and tight approximation ratio is found. To this end, a greedy algorithm named Greedy3P4 is first proposed and proved to have a tight approximation ratio of 3/4 for the D1RD-EQ problem. Then, by using Greedy3P4 as a bridge, 3/4 is also proved to be the tight approximation ratio of Greedy2P3E and it is tight for all $n{\geq }2$ . Comparative evaluations are performed on real cases using a real vehicle trajectory dataset. The results show that these greedy algorithms usually return near optimal solutions with a profit more than 98% of the optimal solutions, and the greedy algorithms well outperform the other typical algorithms tested.

中文翻译：

---

一维VANET中用于最优RSU部署的两种贪婪算法的紧逼近比

为了解决一维路边单元部署（D1RD）问题，两年前提出了一种贪婪的近似算法Greedy2P3E，对于具有Eradi半径RSU的D1RD问题，它的近似比至少为2/3（ D1RD-EQ问题）。可以找到更好甚至更近似的Greedy2P3E近似值吗？在本文中，重新检验了Greedy2P3E的近似比率，并找到了紧密的近似比率。为此，首先提出了一种贪婪算法Greedy3P4，它被证明对D1RD-EQ问题具有3/4的紧密逼近比。然后，通过使用Greedy3P4作为桥，也证明了3/4是Greedy2P3E的紧密近似比，并且对于所有$ n {\ geq} 2 $ 。使用真实的车辆轨迹数据集对真实情况进行比较评估。结果表明，这些贪婪算法通常会返回接近最优解，其利润超过最优解的98％，并且贪婪算法的性能远远优于其他典型算法。