Color the Conflict: Enabling Simultaneous Traversal in AIM using Graph Coloring

Conflict resolution, particularly through effective priority assignment and right-of-way negotiation, is a critical factor in maximizing intersection throughput and minimizing vehicle crossing time in Autonomous Intersection Management (AIM). This paper proposes a novel color-based round scheduling algorithm that enables simultaneous traversal of multiple vehicles on both conflicting and non-conflicting paths by segmenting the paths inside the intersection using a graph coloring technique. Unlike traditional approaches that resolve conflicts at each individual conflict point, this method eliminates conflict checking by globally coordinating vehicle movements based on color rounds. As a result, the algorithm significantly reduces computational complexity and the number of conflict comparisons, which otherwise scale exponentially with the number of vehicles and conflict points. Simulations in the CARLA simulator across varying traffic densities and movement scenarios demonstrate that the proposed algorithm improves intersection throughput by up to 343% compared to reservation-based methods using FCFS for priority resolution. It also reduces average crossing time by approximately 76% compared to traditional traffic signals and by 94% relative to standalone FCFS strategies. We have also demonstrated that the proposed algorithm is fair in terms of the number of vehicles crossing the intersection per route.