GRAPH DISTANCES IN THE DATA-STREAM MODEL

Publication Date

2008

Journal or Book Title

SIAM JOURNAL ON COMPUTING

Abstract

We explore problems related to computing graph distances in the data-stream model. The goal is to design algorithms that can process the edges of a graph in an arbitrary order given only a limited amount of working memory. We are motivated by both the practical challenge of processing massive graphs such as the web graph and the desire for a better theoretical understanding of the data- stream model. In particular, we are interested in the trade-offs between model parameters such as per- data-item processing time, total space, and the number of passes that may be taken over the stream. These trade-offs are more apparent when considering graph problems than they were in previous streaming work that solved problems of a statistical nature. Our results include the following: (1) Spanner construction: There exists a single-pass, ˜ O(tn1+1/t)-space, ˜ O(t2n1/t)-time-per-edge Ω(n1+1/k) space. Since constructing BFS trees is an important subroutine in many traditional graph algorithms, this demonstrates the need for new algorithmic techniques when processing graphs in the data-stream model. (3) Graph-distance lower bounds: Any t-approximation of the distance between two nodes requires Ω(n1+1/t) space. We also prove lower bounds for determining the length of the shortest cycle and other graph properties. (4) Techniques for decreasing per-edge processing: We discuss two general techniques for speeding up the per-edge computation time of streaming algorithms while increasing the space by only a small factor.

DOI

http://dx.doi.org/10.1137/070683155

Pages

1709-1727

Volume

38

Issue

5

This document is currently not available here.

Share

COinS