Probabilistic counting algorithms for data base applications
Journal of Computer and System Sciences
Estimating simple functions on the union of data streams
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Join-distinct aggregate estimation over update streams
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Graph distances in the streaming model: the value of space
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Trading off space for passes in graph streaming problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Better size estimation for sparse matrix products
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Intractability of min- and max-cut in streaming graphs
Information Processing Letters
gSketch: on query estimation in graph streams
Proceedings of the VLDB Endowment
| Hi-index | 0.00 |
We consider the updatable streaming graph model, where edges of a graph arrive or depart in arbitrary sequence and are processed in an online fashion using sub-linear space and time. We study the problem of estimating aggregate path metrics Pk defined as the number of pairs of vertices that have a simple path between them of length k. For a streaming undirected graph with n vertices, m edges and r components, we present an $\tilde{O}(m(m-r)^{-1/4})$ space algorithm for estimating P2 and an $\Omega(\sqrt{m})$ space lower bound. We show that estimating P2 over directed streaming graphs, and estimating Pk over streaming graphs (whether directed or undirected), for any k ≥3 requires Ω(n2) space. We also present a space lower bound of Ω(n2) for the problems of (a) deterministically testing the connectivity, and, (b) estimating the size of transitive closure, of undirected streaming graphs that allow both edge-insertions and deletions.