Abstract: Techniques are provided for ranking time-series including previously detected anomalous fact quantity changes over an associated time interval. Time-series are received, and for each time-series, a normalized fact quantity change is determined, and each time-series is ranked based in part on the normalized fact quantity change. A normalized fact quantity change may be determined by determining a normalization factor over the time interval, and then determining a product of the normalization factor and the absolute value of the fact quantity change of that time interval. Alternatively, a normalized fact quantity change may be the product of the normalization factor, a predetermined order factor, and the absolute value of the fact quantity change. The normalization factor is determined by analyzing the distribution of the fact quantity change over dimension values of the dimension(s) associated with the time-series to determine the number of values in which the fact quantity is concentrated.

Abstract: Techniques are provided for ranking time-series including previously detected anomalous fact quantity changes over an associated time interval. Time-series are received, and for each time-series, a normalized fact quantity change is determined, and each time-series is ranked based in part on the normalized fact quantity change. A normalized fact quantity change may be determined by determining a normalization factor over the time interval, and then determining a product of the normalization factor and the absolute value of the fact quantity change of that time interval. Alternatively, a normalized fact quantity change may be the product of the normalization factor, a predetermined order factor, and the absolute value of the fact quantity change. The normalization factor is determined by analyzing the distribution of the fact quantity change over dimension values of the dimension(s) associated with the time-series to determine the number of values in which the fact quantity is concentrated.

Abstract: Zero elements are added to respective lines (e.g., rows/columns) of a sparse matrix. The added zero elements increase the number of elements in the respective lines to be a multiple of a predetermined even number “n” (e.g., 2, 4, 8, etc.), based upon an n-fold unrolling loop, where n=2, 4, 8, etc. By forming a sparse matrix having lines (e.g., rows or columns) that are multiples of the predetermined number “n”, the n-fold unrolling loop thereby acts upon a predetermined number of elements in respective iterations, avoiding unnecessarily costly operations (e.g., additional loop unrolling code) on remainder non-zero elements (e.g. remainder row/column elements not within an n-fold unrolling loop) left in a row or column after unrolling. This improves the efficiency of sparse matrix linear algebra solvers and key sparse linear algebra kernels (e.g., SPMV) thereby improving the overall performance of a computer (e.g., running an application).