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Approximating average parameters of graphs
Author(s) -
Goldreich Oded,
Ron Dana
Publication year - 2008
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Book series
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
ISBN - 3-540-38044-2
DOI - 10.1002/rsa.20203
Subject(s) - sublinear function , combinatorics , vertex (graph theory) , mathematics , oracle , degree (music) , graph , discrete mathematics , computer science , physics , software engineering , acoustics
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. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008