Abstract: A method and system are provided for non-redundant detection of coactively linked nodes/data elements of a network or database topologically disposed in at least one triangularly linked arrangement. The network/database is topologically modelled as a graph having a plurality of vertices connected by edges. A neighborhood is generated in computer readable form for each connected vertex containing all other vertices directly connected thereto as neighbors. Connected vertex are ordered according to degree based on the number of neighbors. A reduced neighborhood is formed for each connected vertex by adaptively removing any lower order neighbor. Triangle neighborhoods are generated responsive to forward detections of common triangle neighbors through pairwise comparisons of reduced neighborhoods for connected vertices and each of their higher order neighbors, and reverse detection for certain connected vertices as triangle neighbors by lower ordered neighbors.

Abstract: A method is disclosed for pairwise combination of data elements of an input data stream. Steps are performed for each data element. A master controller reads the data from the stream and increments a counter. A register is instantiated, holding at least two words of memory and corresponding to the counter, by updating a register map and sending a message to a target processor via a logical pathway. The message instructs the target processor to create the register in local memory, including first and second memory locations, and an index corresponding to a value i. The target processor copies the data into the first memory location. For every other register corresponding to a value less than i, the other register copies the data into the second memory location and outputs a unique pair, constructed from the data elements stored at the first and second memory locations, to a database.

Abstract: A method includes receiving, at a master controller, a matrix representing a graph and a first vector, and initializing a counter variable and an array to track dimensionality reduction for the matrix. The method also includes multiplying a subset of the matrix based on the counter variable, by a subset of the first binary vector based on the counter variable. Multiplying includes providing, the vector and a matrix portion to a first processor, and the vector and another portion of the matrix to a second processor. The method also includes, at the processors, multiplying the vectors by the portions of the matrix and returning the results. The method also includes combining the results at the master controller. The method also includes incrementing the counter variable and updating the tracking array for larger dimensionality reduction of the matrix. The method also includes constructing the logical pathway based on the tracking array.