Abstract: Data are maintained in a distributed computing system that describe a directed graph representing relationships among a set of items. The directed graph models a condition having an associated problem. The directed graph has graph components having associated data fields. The relationships are analyzed to identify a solution to the problem. As part of the analysis, a new value for the data field associated with a graph component is identified responsive to an operation performed during the analysis. The new value is compared with an existing value of the data field, and the data field is modified. The modification may include inserting the new value into an overflow vector of data, and replacing the existing value in the data field with exception information identifying the location of the new value. An exception flag associated with the data field is set to indicate that the exception information is being used.

Abstract: Methods, systems, and apparatus, including computer programs for identifying, using historical interactions associated with a first user, contact groups, where the first user is associated with each contact group, are provided. A score, with respect to a second user, is calculated for each contact group based on an amount of interaction between the second user and the respective contact group, thereby deriving a plurality of scores. A first contact group is determined. The first contact group has a first score in the plurality of scores that satisfies a predetermined threshold. A contact group suggestion is generated, responsive to the determining, that comprises an invitation to add the second user to the first contact group. The first user is notified of the contact group suggestion.

Abstract: Data are maintained in a distributed computing system that describe a directed graph representing relationships among a set of items. The directed graph models a condition having an associated problem. The directed graph has graph components having associated data fields. The relationships are analyzed to identify a solution to the problem. As part of the analysis, a new value for the data field associated with a graph component is identified responsive to an operation performed during the analysis. The new value is compared with an existing value of the data field, and the data field is modified. The modification may include inserting the new value into an overflow vector of data, and replacing the existing value in the data field with exception information identifying the location of the new value. An exception flag associated with the data field is set to indicate that the exception information is being used.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for receiving an identifier associated with a user of a social networking service, identifying one or more first services provided by a first service provider, determining that the user is a user of the one or more first services based on the identifier, identifying first contacts of the user within each of the one or more first services, and generating a social vicinity index based on the first contacts, the social vicinity index including one or more potential contacts for the user within the social networking service.

Abstract: Methods, systems, and apparatus, including computer programs for identifying, using historical interactions associated with a first user, contact groups, where the first user is associated with each contact group, are provided. A score, with respect to a second user, is calculated for each contact group based on an amount of interaction between the second user and the respective contact group, thereby deriving a plurality of scores. A first contact group is determined. The first contact group has a first score in the plurality of scores that satisfies a predetermined threshold. A contact group suggestion is generated, responsive to the determining, that comprises an invitation to add the second user to the first contact group. The first user is notified of the contact group suggestion.

Abstract: Resolving conflicting graph mutations in a distributed computing system. Graph data for at least a partition of a graph is stored in a worker system of a distributed computing system. The graph represents relationships among a set of tangible items that model a real-world condition having an associated problem. A plurality of conflicting mutation requests are received to mutate the graph. A conflict between the mutation requests is resolved with a conflict resolution function that lacks direct access to the graph data. The graph data is updated responsive to a result generated by resolving the conflict using the conflict resolution function.