Methods and systems for optimizing network travel costs

Methods and systems optimize travel costs both on and off a sequence of one or more networks used to represent travel, communication, or transport of anything within a spatial medium. Such systems and methods can develop a data structure for optimizing travel costs for a region having an embedded network. The data structure includes a grid representation of the region having an array of cells covering the region, an optimal-cost grid dataset containing optimal costs for travel between an initial location in the region and cells in the grid, a hybrid grid-network dataset representing travel costs within the network, within the grid, and between the network and the grid, and back-links among elements of the hybrid grid-network dataset, reflecting optimal travel routes originating at the initial location. Methods and systems also include querying the datasets of the data structure to generate a route with an optimal travel cost from the initial location to a query point.