Random sampling in cut, flow, and network design problems
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Approximating s-t minimum cuts in Õ(n2) time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Fast, small-space algorithms for approximate histogram maintenance
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Worst-case update times for fully-dynamic all-pairs shortest paths
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sampling in dynamic data streams and applications
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
Optimal Two-Stage Algorithms for Group Testing Problems
SIAM Journal on Computing
Approximating the Minimum Spanning Tree Weight in Sublinear Time
SIAM Journal on Computing
Summarizing and mining inverse distributions on data streams via dynamic inverse sampling
VLDB '05 Proceedings of the 31st international conference on Very large data bases
On graph problems in a semi-streaming model
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Counting distinct items over update streams
Theoretical Computer Science
Graph Sparsification in the Semi-streaming Model
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Graph Distances in the Data-Stream Model
SIAM Journal on Computing
Optimal sampling from distributed streams
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
1-pass relative-error Lp-sampling with applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Tight bounds for Lp samplers, finding duplicates in streams, and related problems
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Filtering: a method for solving graph problems in MapReduce
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Linear programming in the semi-streaming model with application to the maximum matching problem
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Dynamic Connectivity: Connecting to Networks and Geometry
SIAM Journal on Computing
On the Power of Adaptivity in Sparse Recovery
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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
Weighted Matching in the Semi-Streaming Model
Algorithmica
IEEE Transactions on Information Theory
Graph sketches: sparsification, spanners, and subgraphs
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Graph synopses, sketches, and streams: a survey
Proceedings of the VLDB Endowment
How robust are linear sketches to adaptive inputs?
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Homomorphic fingerprints under misalignments: sketching edit and shift distances
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
ACM Transactions on Database Systems (TODS) - Invited papers issue
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We initiate the study of graph sketching, i.e., algorithms that use a limited number of linear measurements of a graph to determine the properties of the graph. While a graph on n nodes is essentially O(n2)-dimensional, we show the existence of a distribution over random projections into d-dimensional "sketch" space (dn2) such that the relevant properties of the original graph can be inferred from the sketch with high probability. Specifically, we show that: 1. d = O(n · polylog n) suffices to evaluate properties including connectivity, k-connectivity, bipartiteness, and to return any constant approximation of the weight of the minimum spanning tree. 2. d = O(n1+γ) suffices to compute graph sparsifiers, the exact MST, and approximate the maximum weighted matchings if we permit O(1/γ)-round adaptive sketches, i.e., a sequence of projections where each projection may be chosen dependent on the outcome of earlier sketches. Our results have two main applications, both of which have the potential to give rise to fruitful lines of further research. First, our results can be thought of as giving the first compressed-sensing style algorithms for graph data. Secondly, our work initiates the study of dynamic graph streams. There is already extensive literature on processing massive graphs in the data-stream model. However, the existing work focuses on graphs defined by a sequence of inserted edges and does not consider edge deletions. We think this is a curious omission given the existing work on both dynamic graphs in the non-streaming setting and dynamic geometric streaming. Our results include the first dynamic graph semi-streaming algorithms for connectivity, spanning trees, sparsification, and matching problems.