Abstract: Systems and methods are disclosed to implement a bounded group by query system that computes approximate time-sliced statistics for groups of records in a dataset according to a group by query. In embodiments, a single pass scan of the dataset is performed to accumulate exact results for a maximum number of groups in a result grouping structure (RGS) and approximate results for additional groups in an approximate result grouping structure (ARGS). RGSs and ARGSs are accumulated by a set of accumulator nodes and provided to an aggregator node, which combines the received structures to generate exact or approximate statistical results for at least a subset of the groups in the dataset. Advantageously, the disclosed query system is able to produce approximate results for at least some of the groups in a single pass of the dataset using size-bounded data structures, without predetermining the actual number of groups in the dataset.

Abstract: Systems and methods are disclosed to implement a bounded group by query system that computes approximate time-sliced statistics for groups of records in a dataset according to a group by query. In embodiments, a single pass scan of the dataset is performed to accumulate exact results for a maximum number of groups in a result grouping structure (RGS) and approximate results for additional groups in an approximate result grouping structure (ARGS). RGSs and ARGSs are accumulated by a set of accumulator nodes and provided to an aggregator node, which combines the received structures to generate exact or approximate statistical results for at least a subset of the groups in the dataset. Advantageously, the disclosed query system is able to produce approximate results for at least some of the groups in a single pass of the dataset using size-bounded data structures, without predetermining the actual number of groups in the dataset.

Abstract: A shoelace with greeting messages imprinted on the surface. The greeting messages can be imprinted on either or both sides of the shoelace. In one embodiment, the greeting message includes two parts, namely, a first part similar to messages on the outside of a normal greeting card and a second part similar to messages on the inside of a normal greeting card.