Dynamic Graphs in the Sliding-Window Model

We present the first algorithms for processing graphs in the sliding-window model. The sliding window model, introduced by Datar et al. (SICOMP 2002), has become a popular model for processing infinite data streams in small space when older data items (i.e., those that predate a sliding window containing the most recent data items) are considered "stale" and should implicitly be ignored. While processing massive graph streams is an active area of research, it was hitherto unknown whether it was possible to analyze graphs in the sliding-window model. We present an extensive set of positive results including algorithms for constructing basic graph synopses like combinatorial sparsifiers and spanners as well as approximating classic graph properties such as the size of a graph matching or minimum spanning tree.