  In this paper, we address a problem of safe and efficient intersection
crossing traffic management of autonomous and connected ground traffic. Toward
this objective, we propose an algorithm that is called the Discrete-time
occupancies trajectory based Intersection traffic Coordination Algorithm
(DICA). We first prove that the basic DICA is deadlock free and also starvation
free. Then, we show that the basic DICA has a computational complexity of
$\mathcal{O}(n^2 L_m^3)$ where $n$ is the number of vehicles granted to cross
an intersection and $L_m$ is the maximum length of intersection crossing
routes.
  To improve the overall computational efficiency of the algorithm, the basic
DICA is enhanced by several computational approaches that are proposed in this
paper. The enhanced algorithm has the computational complexity of
$\mathcal{O}(n^2 L_m \log_2 L_m)$. The improved computational efficiency of the
enhanced algorithm is validated through simulation using an open source traffic
simulator, called the Simulation of Urban MObility (SUMO). The overall
throughput as well as the computational efficiency of the enhanced algorithm
are also compared with those of an optimized traffic light control.
