Optimal and Greedy Algorithms for the One-Dimensional RSU Deployment Problem With New Model

Abstract

Optimal road side unit (RSU) deployment is of crucial importance to vehicular ad hoc networks. The RSU deployment (RD) problem models in the literature usually lack the ability to describe curve-shaped roads and roads nonuniform statistics. We had proposed a more realistic RD problem model taking these features into consideration. However, our understanding of the RD problem with the new model is still seriously limited. In this paper, we try to deepen our understanding of the one-dimensional RD (D1RD) problem with the new model by analyzing its properties and designing optimal and efficient approximate algorithms for it. We first analyze the properties of optimal solutions of the D1RD problem. Next, suspecting that the D1RD problem with $n$ RSUs of different coverage radii is intractable, we propose two greedy-based algorithms (named as Greedy2P3 and Greedy2P3E) and show that Greedy2P3E's approximation ratio is at least $1-(\frac{n-1}{n})^2$ . Then, by exploiting the properties of the D1RD problem, we propose an optimal algorithm named OptGreDyn by combining greedy idea and dynamic programming, and prove its optimality. At last, we proved that, if applied to the RD problem with $n$ RSUs of identical radii, the approximation ratios of Greedy2P3 and Greedy2P3E are at least $\frac{2}{3}$ , and it is tight for Greedy2P3 when $n=3i$ , where $i$ is a positive integer. Simulation results verify the optimality of OptGreDyn, meanwhile show that Greedy2P3 and Greedy2P3E usually return near-optimal solutions with profit more than 98% of the optimal solutions, and they are preferable than the existing approximate algorithms.