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 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.
The research was supported in part by the Israel Internet Association (ISOC-IL).
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Goldreich, O., Ron, D. (2006). Approximating Average Parameters of Graphs . In: Díaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2006 2006. Lecture Notes in Computer Science, vol 4110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11830924_34
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DOI: https://doi.org/10.1007/11830924_34
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