Abstract: Approaches in accordance with various embodiments provide for the processing of sparse matrices for mathematical and programmatic operations. In particular, various embodiments utilize a tiling approach that divides a sparse matrix into submatrices, many of which will include only zero-value entities. These empty tiles can be ignored, and only the tiles with non-zero entries processed, which reduces resource and time requirements for the processing. An indexing approach can be used for each entity that is a combination of the tile identifier and an offset value, which enables the values to be multiplied correctly against, for example, values of a dense matrix. The tiles can be processed in parallel and the results accumulated to generate a matrix product. The matrix product can then be passed to the next step in a process or operation, such as to a next layer in a deep neural network.

Abstract: A system and method is provided for identifying network links for augmentation based on potential link failures. In one aspect, the links are selected by identifying multiple shortest paths between a node pair and generating augmentation recommendations for a single link by accumulating recommendations based on multiple node pairs.

Abstract: A traffic engineering process seeks to optimize network utilization and creating paths in the network such that the network is used efficiently. The exemplary embodiments seek to maintain fairness across allocation of flows while honoring constraints on the number of paths used per flow and the granularity of splits allowed. Exemplary embodiments provide a solution in a speedy manner and get close to optimal solutions for allocation of the network traffic.

Abstract: A system and method is provided for identifying network links for augmentation based on potential link failures. In one aspect, the links are selected by identifying multiple shortest paths between a node pair and generating augmentation recommendations for a single link by accumulating recommendations based on multiple node pairs.

Abstract: Systems and methods are disclosed herein for measuring the traffic flow on a link. The system includes a processor that is configured to generate aggregate egress data for multiple origin endpoints by aggregating amounts of egress traffic detected by servers processing the egress traffic at the origin endpoints. The processor is also configured to obtain the proportions of traffic flows that traverse each path between each endpoint pair, which includes an origin endpoint and a destination endpoint. Each path includes multiple network links such that a single network link may be shared across multiple paths. Finally, the processor computes an amount of traffic flow on a shared link based on the aggregate egress data and the obtained proportions.

Abstract: Systems and methods for optimizing traffic in a data network. Network traffic may be optimized by associating costs with data links that connect network nodes. A set of lowest cost paths between a source network node and a destination network node may be determined by analyzing paths in the data network. An explored path may be extended to another network node based on whether the other network node is able to reach the destination network node without forming a loop with the explored path.