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Estimating Simple Graph Parameters in Sublinear Time

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  • First Online:
Encyclopedia of Algorithms

  • 61 Accesses

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...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel

    Oded Goldreich

  2. School of Electrical Engineering, Tel-Aviv University, Ramat-Aviv, Israel

    Dana Ron

Authors
  1. Oded Goldreich
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  2. Dana Ron
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Corresponding author

Correspondence to Oded Goldreich .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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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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