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Mikhail Kapralov

Rina Panigrahy

A sparsifier is generated from a union of multiple spanners of a graph. The edges of the sparsifier are weighted based on a measure of connectivity called robust connectivity. The robust connectivity of a node pair is the highest edge sampling probability at which a distance between the pair is likely to drop below a specified length. Each spanner is generated from a subgraph of the graph that is generated using a decreasing sampling probability. For the weight of each edge, a spanner is determined where an estimated distance between the nodes associated with the edge is greater than a threshold distance. The sampling probability of the subgraph used to generate the spanner is an estimate of the robust connectivity of the edge. The weight of the edge is set to the inverse of the estimated robust connectivity.

Generating a sparsifier using graph spanners

Multiple data prediction strategies are received. Each data prediction strategy may predict a next data value in a sequence of data values with a corresponding confidence value. Rather than rely on a single prediction strategy, the predictions of each of the data prediction strategies are linearly combined to generate a single prediction that is more accurate and has a lower overall loss than any of the individual prediction strategies. Further, a deviation is calculated based on the values in the sequence of values that have been observed so far using a weighted sum that favors more recent values in the sequence over less recent values in the sequence. A prediction of the next value in the sequence is generated based on the combined strategies and the calculated deviation.

Predicting values in sequence

To facilitate the estimation of relatedness between nodes of a graph, implementations estimate relatedness between nodes in a graph by pre-computing for a subset of sample nodes (e.g., center nodes) a plurality of transition probabilities between each sample node and each of the other nodes in the graph, and then later when queried the implementations calculate in real-time the resultant estimated transition probability between the first node and the second node through the at least one sample node based on the pre-computed transition probabilities.

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Stanford, CA, United States of America

Mikhail Kapralov