Final answer:
A Planarity Algorithm is a method for determining whether a graph can be drawn on a plane without intersecting edges. The Hopcroft-Tarjan algorithm is a popular algorithm for testing planarity. It uses an ordering of vertices and depth-first search to check for intersections between edges.
Step-by-step explanation:
A Planarity Algorithm is a method that determines whether a graph can be drawn on a plane without any of its edges intersecting. One popular algorithm for testing planarity is the Hopcroft-Tarjan algorithm, which has a time complexity of O(n log n). This algorithm works by assigning an ordering to the vertices and then recursively checking for intersections between edges using depth-first search. If no intersections are found, the graph is planar.
To apply the Hopcroft-Tarjan algorithm, follow these steps:
- Assign an ordering to the vertices.
- Perform a depth-first search to find intersections between edges.
- If any intersections are found, the graph is not planar.
- If no intersections are found, the graph is planar.