This document discloses a system that selects a path to reach a destination in a transportation network. The system receives information related to a public transportation network with multiple stops. Each stop includes at least one associated link with another stop. Each link represents a mode of transportation between two stops. When the system receives a request for routes between an origin and a destination within the transportation network, it will determine a set of routes between the origin and the destination using an iterative process without reference to a graph representation of the network. The system will select a shortest path that corresponds to the route having the earliest arrival time at the destination. The system will also select an alternative path that corresponds to a route having an arrival time that is no more than a threshold amount later than the earliest arrival time.