SIAM Journal on Computing
A spectrum of time-space trade-offs for undirected s-tconnectivity
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
External memory algorithms
Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Reductions in streaming algorithms, with an application to counting triangles in graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Testing Random Variables for Independence and Identity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Optimal space lower bounds for all frequency moments
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A uniform approach to accelerated PageRank computation
WWW '05 Proceedings of the 14th international conference on World Wide Web
Space efficient mining of multigraph 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
Simpler algorithm for estimating frequency moments of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Trading off space for passes in graph streaming problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Streaming and sublinear approximation of entropy and information distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
To randomize or not to randomize: space optimal summaries for hyperlink analysis
Proceedings of the 15th international conference on World Wide Web
Counting triangles in data streams
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Approximate quantiles and the order of the stream
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Local Graph Partitioning using PageRank Vectors
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Estimating entropy over data streams
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Parallelizing the computation of PageRank
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
New streaming algorithms for counting triangles in graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Finding graph matchings in data streams
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Lower bounds for quantile estimation in random-order and multi-pass streaming
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Proceedings of the 28th ACM symposium on Principles of distributed computing
Efficient distributed random walks with applications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Fast nearest-neighbor search in disk-resident graphs
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Fast incremental and personalized PageRank
Proceedings of the VLDB Endowment
Fast personalized PageRank on MapReduce
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Buyback problem: approximate matroid intersection with cancellation costs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Multiplicative approximations of random walk transition probabilities
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
gSketch: on query estimation in graph streams
Proceedings of the VLDB Endowment
Approximate computation and implicit regularization for very large-scale data analysis
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Space-efficient sampling from social activity streams
Proceedings of the 1st International Workshop on Big Data, Streams and Heterogeneous Source Mining: Algorithms, Systems, Programming Models and Applications
On the efficiency of estimating penetrating rank on large graphs
SSDBM'12 Proceedings of the 24th international conference on Scientific and Statistical Database Management
Dynamic pagerank using evolving teleportation
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
Facilitating real-time graph mining
Proceedings of the fourth international workshop on Cloud data management
DrunkardMob: billions of random walks on just a PC
Proceedings of the 7th ACM conference on Recommender systems
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This study focuses on computations on large graphs (e.g., the web-graph) where the edges of the graph are presented as a stream. The objective in the streaming model is to use small amount of memory (preferably sub-linear in the number of nodes n) and a few passes. In the streaming model, we show how to perform several graph computations including estimating the probability distribution after a random walk of length l, mixing time, and the conductance. We estimate the mixing time M of a random walk in Õ(nα+Mα√n+√Mn/ α) space and Õ(√Mα) passes. Furthermore, the relation between mixing time and conductance gives us an estimate for the conductance of the graph. By applying our algorithm for computing probability distribution on the web-graph, we can estimate the PageRank p of any node up to an additive error of √εp in Õ(√M/α) passes and Õ(min(nα + 1/ε √M/α + 1/ε Mα, αn√Mα + 1/ε √M/α)) space, for any α ∈ (0, 1]. In particular, for ε = M/n, by setting α = M--1/2, we can compute the approximate PageRank values in Õ(nM--1/4) space and Õ(M3/4) passes. In comparison, a standard implementation of the PageRank algorithm will take O(n) space and O(M) passes.