Approximating Average Parameters of Graphs

Webpage for a paper by Oded Goldreich and Dana Ron


Inspired by Feige (36th STOC, 2004), we initiate a study of sublinear randomized algorithms for approximating average parameters of a graph. Specifically, we consider the average degree of a graph and the average distance between pairs of vertices in a graph. Since our focus is on sublinear algorithms, these algorithms access the input graph via queries to an adequate oracle. We consider two types of queries. The first type is standard neighborhood queries (i.e., "what is the $i$th neighbor of vertex $v$?"), whereas the second type are queries regarding the quantities that we need to find the average of (i.e., "what is the degree of vertex $v$?" and "what is the distance between $u$ and $v$?", respectively). Loosely speaking, our results indicate a difference between the two problems: For approximating the average degree, the standard neighbor queries suffice and in fact are preferable to degree queries. In contrast, for approximating average distances, the standard neighbor queries are of little help whereas distance queries are crucial.

Note: Part of this work appeared in our work On Estimating the Average Degree of a Graph.

Note: This work may be viewed as initiating a wider study, concerned with the fast approximation of various averages. See, for example, a follow-up work on approximating the average distance between points in metric spaces.

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