Contents I. Introduction
Batch is an important pattern in data streams [2], which is a group of identical items that arrive closely. Two adjacent batches of the same item are spaced by a minimum interval \$\mathcal{T}\$, where \$\mathcal{T}\$ is a predefined threshold. Although batches can make a difference in various applications, such as cache [2], networks [3], and machine learning [4], [5], it is not enough to just study batches. For instance, in cache systems, with just the measurement results of batches, we are still not able to devise any prefetching method and replacement policy. Further mining some special patterns of batches is of great importance. On the basis of batches, we propose a new pattern, namely periodic batch. A group of periodic batches refers to \$\alpha\$ consecutive batches of the same item, where these batches arrive periodically. We call \$\alpha\$ the periodicity. Finding top-\$k\$ periodic batches refers to reporting \$k\$ groups of periodic batches with the \$k\$ largest periodicities.
