Abstract: In some implementations, a computing device can present alight notifications to a user when the user (e.g., user device) is approaching a public transit stop where the user should depart the public transit vehicle the user is currently occupying. For example, a user may use a user device to generate a public transit route that includes a starting location, a sequence of public transit stops, and a destination location. While traversing the transit route, the user may need to exit public transit vehicle (e.g., to reach the destination location, to switch transit lines, etc.). The user device can identify transit stops along the route where the user should exit a transit vehicle and present notifications prompting the user to exit the transit vehicle at the upcoming stop as the user device approaches the identified transit stops.

Abstract: Distance query techniques are provided that are robust to network structure, scale to large and massive networks, and are fast, straightforward, and efficient. A hierarchical hub labeling (HHL) technique is described to determine a distance between two nodes or vertices on a network. The HHL technique provides indexing by ordering vertices by importance, then transforming the ordering into an index, which enables fast exact shortest-path distance queries. The index may be compressed without sacrificing its correctness.

Abstract: A graph that includes multiple nodes and edges is received. Multiple instances of the graph are generated by randomly instantiating the edges according to either a binary independent cascade model or a randomized edge length independent cascade model. Where the binary independent cascade model is used, combined reachability sketches are generated for each node across all instances of the graph. Where the randomized edge length independent cascade model is used, combined all-distances sketches are generated for each node across all instances of the graph. Depending on which model is used, the combined reachability or all-distances sketches are used to estimate the influence of nodes in the graph or to estimate a subset of nodes from a graph of a specified size with a maximum influence using a greedy algorithm.

Abstract: A graph that includes multiple nodes and edges is received. Multiple instances of the graph are generated by randomly instantiating the edges according to either a binary independent cascade model or a randomized edge length independent cascade model. Where the binary independent cascade model is used, combined reachability sketches are generated for each node across all instances of the graph. Where the randomized edge length independent cascade model is used, combined all-distances sketches are generated for each node across all instances of the graph. Depending on which model is used, the combined reachability or all-distances sketches are used to estimate the influence of nodes in the graph or to estimate a subset of nodes from a graph of a specified size with a maximum influence using a greedy algorithm.

Abstract: A graph that includes multiple nodes and edges is received. Multiple instances of the graph are generated by randomly instantiating the edges according to either a binary independent cascade model or a randomized edge length independent cascade model. Where the binary independent cascade model is used, combined reachability sketches are generated for each node across all instances of the graph. Where the randomized edge length independent cascade model is used, combined all-distances sketches are generated for each node across all instances of the graph. Depending on which model is used, the combined reachability or all-distances sketches are used to estimate the influence of nodes in the graph or to estimate a subset of nodes from a graph of a specified size with a maximum influence using a greedy algorithm.

Abstract: Distance query techniques are provided that are robust to network structure, scale to large and massive networks, and are fast, straightforward, and efficient. A hierarchical hub labeling (HHL) technique is described to determine a distance between two nodes or vertices on a network. The HHL technique provides indexing by ordering vertices by importance, then transforming the ordering into an index, which enables fast exact shortest-path distance queries. The index may be compressed without sacrificing its correctness.

Abstract: Optimum journeys in public transportation networks are determined. The determination of Pareto optimal journeys from one stop to another stop in a public transportation network uses the criteria travel time and minimum transfers. A technique for bi-criteria journey planning using the aforementioned criteria in public transportation networks operates in rounds (K rounds at most), where after round k (k?K), arrival times are computed for the stops that can be reached with up to k trips.

Abstract: Optimum journeys in public transportation networks are determined. The determination of Pareto optimal journeys from one stop to another stop in a public transportation network uses the criteria travel time and minimum transfers. A technique for bi-criteria journey planning using the aforementioned criteria in public transportation networks operates in rounds (K rounds at most), where after round k (k?K), arrival times are computed for the stops that can be reached with up to k trips.

Abstract: A point-to-point shortest path technique supports real-time queries and fast metric update or replacement (metric customization). Arbitrary metrics (cost functions) are supported without significant degradation in performance. Determining a shortest path between two locations uses three stages: a preprocessing stage, a metric customization stage, and a query stage. Preprocessing is based on a graph structure only, while metric customization augments preprocessing results taking edge costs into account. The preprocessing partitions the graph into loosely connected components of bounded size and creates an overlay graph by replacing each component with a “clique” connecting its boundary vertices. Clique edge lengths are computed during the customization phase. The customization phase can be repeated for various different metrics, and produces a small amount of data for each. The query phase is run using the metric-independent data together with the relevant metric-specific data.