Tight Approximation Ratios of Two Greedy Algorithms for Optimal RSU Deployment in One-Dimensional VANETs

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.