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Independent Set Size Approximation in Graph Streams
We study the problem of estimating the size of independent sets in a graph
defined by a stream of edges. Our approach relies on the Caro-Wei bound,
which expresses the desired quantity in terms of a sum over nodes of the
reciprocal of their degrees, denoted by . Our results show that
can be approximated accurately, based on a provided lower bound on
. Stronger results are possible when the edges are promised to arrive
grouped by an incident node. In this setting, we obtain a value that is at most
a logarithmic factor below the true value of and no more than the true
independent set size. To justify the form of this bound, we also show an
lower bound on any algorithm that approximates up to
a constant factor