Years and Authors of Summarized Original Work
2008; Goldreich, Ron
Problem Definition
A graph parameter\(\sigma\) is a real-valued function over graphs that is invariant under graph isomorphism. For example, the average degree of the graph, the average distance between pairs of vertices, and the minimum size of a vertex cover are graph parameters. For a fixed graph parameter \(\sigma\) and a graph G = (V, E), we would like to compute an estimate of \(\sigma (G)\). To this end we are given query access to G and would like to perform this task in time that is sublinear in the size of the graph and with high success probability. In particular, this means that we do not read the entire graph but rather only access (random) parts of it (via the query mechanism). Our main focus here is on a very basic graph parameter: its average degree, denoted \(\overline{d}(G)\).
The estimation algorithm is given an approximation parameter ε > 0. It should output a value \(\hat{d}\)such that with...
Keywords
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Goldreich, O., Ron, D. (2016). Estimating Simple Graph Parameters in Sublinear Time. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_703
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