  \emph{Coresets} are important tools to generate concise summaries of massive
datasets for approximate analysis. A coreset is a small subset of points
extracted from the original point set such that certain geometric properties
are preserved with provable guarantees. This paper investigates the problem of
maintaining a coreset to preserve the minimum enclosing ball (MEB) for a
sliding window of points that are continuously updated in a data stream.
Although the problem has been extensively studied in batch and append-only
streaming settings, no efficient sliding-window solution is available yet. In
this work, we first introduce an algorithm, called AOMEB, to build a coreset
for MEB in an append-only stream. AOMEB improves the practical performance of
the state-of-the-art algorithm while having the same approximation ratio.
Furthermore, using AOMEB as a building block, we propose two novel algorithms,
namely SWMEB and SWMEB+, to maintain coresets for MEB over the sliding window
with constant approximation ratios. The proposed algorithms also support
coresets for MEB in a reproducing kernel Hilbert space (RKHS). Finally,
extensive experiments on real-world and synthetic datasets demonstrate that
SWMEB and SWMEB+ achieve speedups of up to four orders of magnitude over the
state-of-the-art batch algorithm while providing coresets for MEB with rather
small errors compared to the optimal ones.
