Approximating average parameters of graphs

Authors:
Oded Goldreich;Dana Ron
Affiliations:
Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel;Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv, Israel
Venue:
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Year:
2006

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Abstract

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 ithneighbor 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 uand 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.