The paper "Compass Routing on Geometric Networks" by Evangelos Kranakis, Harvinder Singh, and Jorge Urrutia explores a method for navigating geometric networks, specifically focusing on compass routing. The authors model city maps as geometric graphs where street intersections are vertices and streets are straight line segments. Compass routing is an algorithm that guides a traveler from an initial vertex \( s \) to a destination vertex \( t \) by always choosing the edge with the closest slope to the line segment connecting the current position to the destination. The paper introduces the concept of local routing algorithms, which are restricted to using only local information at each vertex and do not change this information once it is stored. The authors aim to develop routing algorithms suitable for existing communication networks, particularly planar networks, and discuss the limitations of previous approaches. They prove that Delaunay triangulations of point sets on the plane support compass routing and present a geometric local routing algorithm that always finds a path between any two vertices of a connected geometric graph. The paper also investigates which planar graphs have embeddings that support shortest path compass routing, concluding that trees always have such embeddings but not all outerplanar graphs or planar graphs do.The paper "Compass Routing on Geometric Networks" by Evangelos Kranakis, Harvinder Singh, and Jorge Urrutia explores a method for navigating geometric networks, specifically focusing on compass routing. The authors model city maps as geometric graphs where street intersections are vertices and streets are straight line segments. Compass routing is an algorithm that guides a traveler from an initial vertex \( s \) to a destination vertex \( t \) by always choosing the edge with the closest slope to the line segment connecting the current position to the destination. The paper introduces the concept of local routing algorithms, which are restricted to using only local information at each vertex and do not change this information once it is stored. The authors aim to develop routing algorithms suitable for existing communication networks, particularly planar networks, and discuss the limitations of previous approaches. They prove that Delaunay triangulations of point sets on the plane support compass routing and present a geometric local routing algorithm that always finds a path between any two vertices of a connected geometric graph. The paper also investigates which planar graphs have embeddings that support shortest path compass routing, concluding that trees always have such embeddings but not all outerplanar graphs or planar graphs do.