Abstract: Graph partitioning for massive scale graphs is described, such as for graphs having vertices representing people and edges representing connections between people in a social networking system; or for graphs where the vertices represent other items and the edges represent relationships between the items. In various embodiments a graph data allocator receives a graph vertex and its edges and allocates the vertex to one of a plurality of clusters each associated with one or more computing devices. In various embodiments the allocation is made by optimizing an objective function which takes into account both a cost of edges between clusters and a cost related to sizes of the clusters. In some examples the cost related to sizes of the clusters comprises a convex function applied to each of the cluster sizes. In examples, computations on the graph data are carried out with reduced runtimes and communications cost.

Abstract: A multiple independent narrow-channel wireless network and method for transmitting and received data over a wireless network using a fragmented frequency spectrum. The system and method uses a plurality of narrow wireless channels obtained from splitting a wide wireless channel. Each narrow channel performs sending, receiving, and carrier sensing. Moreover, each narrow channel is independent such that data can be sent or received without any interference from other narrow channels and without synchronization. Embodiments of the system and method include a compound radio having a compound receiver and a compound transmitter. The compound transmitter includes an inter-radiolet symbol synchronization module, to permit use of a single inverse fast Fourier transform block, and a dynamically configurable filter array, to mitigate leakage between channels. The compound receiver uses fraction data rate processing to optimize efficiency.

Abstract: The claimed subject matter provides a method for wireless communications. The method includes transmitting, by a first node in a wireless network, a first preamble. The method also includes detecting, in parallel with transmitting the first preamble, a transmission of a second preamble. A second node in the wireless network transmits the second preamble. Additionally, the method includes determining a later start between the transmission of the first preamble and the transmission of the second preamble. The method further includes terminating transmission of the first preamble the determining indicates that the transmission of the first preamble started after the transmission of the second preamble.