We study the problem of estimating the size of independent sets in a graph G 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 β(G). Our results show that β(G) can be approximated accurately, based on a provided lower bound on β. 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 β and no more than the true independent set size. To justify the form of this bound, we also show an Ω(n/β) lower bound on any algorithm that approximates β up to a constant factor.
al. REF provide guarantees for estimating the cardinality of a maximum independent set of general graphs via the Caro-Wei bound.
Independent Set Size Approximation in Graph Streams
ArXiv
ArXiv
Mathematics Computer Science