Abstract: One or more all-distances sketches are generated for nodes in a graph. An all-distances sketch for a node includes a subset of the nodes of the graph, and a shortest distance between the node and each of the nodes in the subset of nodes. The generated all-distances sketches are used to estimate the closeness similarity of nodes. The estimated closeness similarity can be used for targeted advertising or for content item recommendation, for example.

Abstract: One or more techniques and/or systems are provided for controlling a travel route planning module associated with a user device. Travel related data, for a user and regarding previously traveled routes by the user, may be indicative of user travel preferences and/or behaviors. The travel related data is evaluated against computed routes derived from different weighting values applied to travel metrics (e.g., a cost associated with a U-turn, a highway, an industrial zone, etc.). For example, weighting values may be iteratively adjusted to generate a plurality of modified computed routes that may be evaluated to identify a target computed route having a similarity to a previously traveled route of the user above a threshold. User preference weighted travel metrics, generated based upon weighted travel metrics of the target computed route, are used to control a travel route planning module to generate a customized travel route for the user.

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: One or more techniques and/or systems are provided for controlling a travel route planning module associated with a user device. Travel related data, for a user and regarding previously traveled routes by the user, may be indicative of user travel preferences and/or behaviors. The travel related data is evaluated against computed routes derived from different weighting values applied to travel metrics (e.g., a cost associated with a U-turn, a highway, an industrial zone, etc.). For example, weighting values may be iteratively adjusted to generate a plurality of modified computed routes that may be evaluated to identify a target computed route having a similarity to a previously traveled route of the user above a threshold. User preference weighted travel metrics, generated based upon weighted travel metrics of the target computed route, are used to control a travel route planning module to generate a customized travel route for the user.

Abstract: One or more all-distances sketches are generated for nodes in a graph. An all-distances sketch for a node includes a subset of the nodes of the graph, and a shortest distance between the node and each of the nodes in the subset of nodes. The generated all-distances sketches are used to estimate the closeness similarity of nodes. The estimated closeness similarity can be used for targeted advertising or for content item recommendation, for example.

Abstract: A point-to-point shortest path technique supports real-time queries and fast metric update or replacement (metric customization). Determining a shortest path between two locations uses three stages: a preprocessing stage, a metric customization stage, and a query stage. Extensions to the customizable route planning (CRP) technique for routing are provided. These extensions include, for example, the computation of alternative routes, faster techniques for unpacking shortcuts, efficient query techniques for batched shortest path (one-to-many, many-to-many, and points of interest) determinations, and determining routes and alternative routes using traffic information.

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: Techniques are described for graph partitioning, and in particular, graph bisection. A lower bound is provided that is computed in near-linear time. These bounds may be used to determine optimum solutions to real-world graphs with many vertices (e.g., more than a million for road networks, or tens of thousands for VLSI and mesh instances). A packing lower bound technique determines lower bounds in a branch-and-bound tree, reducing the number of tree nodes. Techniques are employed to assign vertices without branching on them, again reducing the size of the tree. Decomposition is provided to translate an input graph into less complex subproblems. The decomposition boosts performance and determines the optimum solution to an input by solving subproblems independently. The subproblems can be solved independently using a branch-and-bound approach to determine the optimum bisection.

Abstract: Graph partitioning techniques are based on the notion of natural cuts. A filtering phase performs a series of minimum cut computations to identify and contract dense regions of the graph. This reduces the graph size significantly, but preserves its general structure. An assembly phase uses a combination of greedy and local search heuristics to assemble the final partition. The techniques may be used on road networks, which have an abundance of natural cuts (such as bridges, mountain passes, and ferries).

Abstract: A point-to-point shortest path technique supports real-time queries and fast metric update or replacement (metric customization). Determining a shortest path between two locations uses three stages: a preprocessing stage, a metric customization stage, and a query stage. Extensions to the customizable route planning (CRP) technique for routing are provided. These extensions include, for example, the computation of alternative routes, faster techniques for unpacking shortcuts, efficient query techniques for batched shortest path (one-to-many, many-to-many, and points of interest) determinations, and determining routes and alternative routes using traffic information.

Abstract: Alternative routes to an optimal route may be determined and presented to a user via a computing device. Alternative routes are selected from candidate routes that meet admissibility criteria. In an implementation, admissibility of a candidate route (in order for it to be considered an alternative route) may be determined based on three criteria: “limited sharing”, “local optimality”, and “stretch” such as “uniformly bounded stretch”. Limited sharing refers to the amount of difference between the alternative route and the optimal route, local optimality refers to lack of unnecessary detours, and uniformly bounded stretch refers to a length of the shortest path to travel between two points on the alternative route.

Abstract: Techniques are described for graph partitioning, and in particular, graph bisection. A lower bound is provided that is computed in near-linear time. These bounds may be used to determine optimum solutions to real-world graphs with many vertices (e.g., more than a million for road networks, or tens of thousands for VLSI and mesh instances). A packing lower bound technique determines lower bounds in a branch-and-bound tree, reducing the number of tree nodes. Techniques are employed to assign vertices without branching on them, again reducing the size of the tree. Decomposition is provided to translate an input graph into less complex subproblems. The decomposition boosts performance and determines the optimum solution to an input by solving subproblems independently. The subproblems can be solved independently using a branch-and-bound approach to determine the optimum bisection.

Abstract: Hub based labeling is used to determine a shortest path between two locations. Every point has a label, which consists of a set of hubs along with the distance from the point to all those hubs. The hubs are determined that intersect the two labels, and this information is used to find the shortest distance. A hub based labeling technique uses a preprocessing stage and a query stage. Finding the hubs is performed in the preprocessing stage, and finding the intersecting hubs (i.e., the common hubs they share) is performed in the query stage. During preprocessing, a forward label and a reverse label are defined for each vertex. A query is processed using the labels to determine the shortest path. Hub label compression may be used to preserve the use of labels but reduce space usage.

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 batched shortest path problem, such as a one-to-many problem, is solved on a graph by using a preprocessing phase, a target selection phase, and then, in a query phase, computing the distances from a given source in the graph with a linear sweep over all the vertices. Contraction hierarchies may be used in the preprocessing phase and in the query phase. Optimizations may include reordering the vertices in advance to exploit locality and using parallelism.

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: The non-negative single-source shortest path (NSSP) problem is solved on a graph by using a preprocessing phase and then, in a query phase, computing the distances from a given source in the graph with a linear sweep over all the vertices. Contraction hierarchies may be used in the preprocessing phase and in the query phase. Optimizations may include reordering the vertices in advance to exploit locality, performing multiple NSSP computations simultaneously, marking vertices during initialization, and using parallelism. Techniques may be performed on a graphics processing unit (GPU). This makes applications based on all-pairs shortest-paths practical for continental-sized road networks. The applications include, for example, computing graph diameter, exact arc flags, and centrality measures such as exact reaches or betweenness.

Abstract: Systems and methods are provided for pricing, selling, and/or otherwise distributing electronic content using auction mechanisms. A randomized auction mechanism is used to determine both the number of goods that are sold and the selling price. The auction mechanism automatically adapts to the bid distribution to yield revenue that is competitive with that which could be obtained if the vendor were able to determine the optimal fixed price for the goods. In one embodiment a set of bids is randomly or quasi-randomly partitioned into two or more groups. An optimal threshold is determined for each group, and this threshold is then used to select winning bids from one or more of the other groups. In another embodiment, each bid is compared to a competing bid that is randomly or quasi-randomly selected from the set of bids. If the bid is less than the randomly-selected competing bid, the bid is rejected. Otherwise, the bid is accepted and the bidder buys the auctioned item at the price of the randomly-selected bid.

Abstract: Systems and methods are provided for pricing, selling, and/or otherwise distributing electronic content using auction mechanisms. A randomized auction mechanism is used to determine both the number of goods that are sold and the selling price. The auction mechanism automatically adapts to the bid distribution to yield revenue that is competitive with that which could be obtained if the vendor were able to determine the optimal fixed price for the goods. In one embodiment a set of bids is randomly or quasi-randomly partitioned into two or more groups. An optimal threshold is determined for each group, and this threshold is then used to select winning bids from one or more of the other groups. In another embodiment, each bid is compared to a competing bid that is randomly or quasi-randomly selected from the set of bids. If the bid is less than the randomly-selected competing bid, the bid is rejected. Otherwise, the bid is accepted and the bidder buys the auctioned item at the price of the randomly-selected bid.

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.