Signal Phase Design as Graph Coloring

Coloring Conflicts into Phases

An intersection contains several traffic streams that would like to move at the same time. The problem of signal phase design is to allow compatible streams together while separating movements whose paths cross. The video turns that spatial safety rule into a graph problem.

Each straight or left-turn movement becomes a node. When two movements cannot run together, an edge joins their nodes. Giving compatible movements the same phase is then like assigning the same color to nodes with no edge between them. The animation builds this correspondence one conflict at a time, then shows two familiar ways to organize a standard crossroads: separate turning and through movements, or combine nonconflicting ones. The insight is that phase design is a question of conflict structure, not simply a fixed list of conventional signal sequences. Graph coloring makes that structure explicit and provides a way to search for a compact, safe set of phases.