Rounds in communication complexity revisited
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Communication complexity
Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
Near-Linear Time Construction of Sparse Neighborhood Covers
SIAM Journal on Computing
Some bounds on multiparty communication complexity of pointer jumping
Computational Complexity
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
The communication complexity of pointer chasing
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Fast, small-space algorithms for approximate histogram maintenance
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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
An Approximate L1-Difference Algorithm for Massive Data Streams
SIAM Journal on Computing
Pass efficient algorithms for approximating large matrices
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Surfing Wavelets on Streams: One-Pass Summaries for Approximate Aggregate Queries
Proceedings of the 27th International Conference on Very Large Data Bases
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Stable distributions, pseudorandom generators, embeddings and data stream computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Efficient algorithms for constructing (1+,ε, β)-spanners in the distributed and streaming models
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
A simple linear time algorithm for computing a (2k - 1)-spanner of o(n1+1/k) size in weighted graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Multi-pass geometric algorithms
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Space efficient mining of multigraph streams
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Trading off space for passes in graph streaming problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The space complexity of pass-efficient algorithms for clustering
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
Estimating statistical aggregates on probabilistic data streams
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A near-optimal distributed fully dynamic algorithm for maintaining sparse spanners
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Optimal per-edge processing times in the semi-streaming model
Information Processing Letters
Declaring independence via the sketching of sketches
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Streaming algorithm for graph spanners---single pass and constant processing time per edge
Information Processing Letters
Robust lower bounds for communication and stream computation
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Estimating PageRank on graph streams
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Distributed algorithms for ultrasparse spanners and linear size skeletons
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Estimating statistical aggregates on probabilistic data streams
ACM Transactions on Database Systems (TODS)
New results for finding common neighborhoods in massive graphs in the data stream model
Theoretical Computer Science
Optimal sampling from sliding windows
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Small stretch (α,β)-spanners in the streaming model
Theoretical Computer Science
Trading off space for passes in graph streaming problems
ACM Transactions on Algorithms (TALG)
A sketch-based distance oracle for web-scale graphs
Proceedings of the third ACM international conference on Web search and data mining
Small stretch spanners in the streaming model: new algorithms and experiments
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Adapting parallel algorithms to the W-Stream model, with applications to graph problems
Theoretical Computer Science
Computing graph spanners in small memory: fault-tolerance and streaming
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Intractability of min- and max-cut in streaming graphs
Information Processing Letters
Theoretical Computer Science
Estimating PageRank on graph streams
Journal of the ACM (JACM)
Computing strongly connected components in the streaming model
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
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
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
On estimating path aggregates over streaming graphs
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
The relationship between inner product and counting cycles
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Adapting parallel algorithms to the W-stream model, with applications to graph problems
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Streaming algorithms measured in terms of the computed quantity
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Approximate shortest paths guided by a small index
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
StreamEB: stream edge bundling
GD'12 Proceedings of the 20th international conference on Graph Drawing
Approximating semi-matchings in streaming and in two-party communication
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We investigate the importance of space when solving problems based on graph distance in the streaming model. In this model, the input graph is presented as a stream of edges in an arbitrary order. The main computational restriction of the model is that we have limited space and therefore cannot store all the streamed data; we are forced to make space-efficient summaries of the data as we go along. For a graph of n vertices and m edges, we show that testing many graph properties, including connectivity (ergo any reasonable decision problem about distances) and bipartiteness, requires Ω(n) bits of space. Given this, we then investigate how the power of the model increases as we relax our space restriction. Our main result is an efficient randomized algorithm that constructs a (2t + 1)-spanner in one pass. With high probability, it uses O(t .n1+1/t log2n) bits of space and processes each edge in the stream in O(t2·n1/t log n) time. We find approximations to diameter and girth via the constructed spanner. For t = Ω(log n/log log n), the space requirement of the algorithm is O(n .polylog n), and the per-edge processing time is O(polylog n). We also show a corresponding lower bound of t for the approximation ratio achievable when the space restriction is O(t.n1+1/t log2n).We then consider the scenario in which we are allowed multiple passes over the input stream. Here, we investigate whether allowing these extra passes will compensate for a given space restriction. We show that finding vertices at distance d from a particular vertex will always take d passes, for all d ∈ {1,...,t/2}, when the space restriction is o(n1+1/t). For girth, we show the existence of a direct trade-off between space and passes in the form of a lower bound on the product of the space requirement and number of passes. Finally, we conclude with two general techniques for speeding up the per-edge computation time of streaming algorithms while increasing the space by at most a log factor.