## G. Cormode, M. Mitzenmacher, and J. Thaler.
Streaming graph computations with a helpful advisor.
*Algorithmica*, 65(2):409-442, 2013.

Motivated by the trend to outsource work to commercial cloud computing
services, we consider a variation of the streaming paradigm where a
streaming algorithm can be assisted by a powerful helper that can
provide annotations to the data stream. We extend previous work on
such *annotation models* by considering a number of graph
streaming problems. Without annotations, streaming algorithms for
graph problems generally require significant memory; we show that
for many standard problems, including all graph problems that can
be expressed with totally unimodular integer programming formulations,
only constant space (measured in words) is
needed for single-pass algorithms given linear-sized annotations.
We also obtain protocols achieving essentially *optimal* tradeoffs between
annotation length and memory usage for several important problems, including
integer matrix-vector multiplication, as well as
shortest *s*-*t* path in small-diameter graphs. We also obtain non-trivial tradeoffs for minimum
weight bipartite perfect matching and shortest *s*-*t* path in general graphs.

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