A faster algorithm for finding the minimum cut in a graph
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Random sampling in cut, flow, and network design problems
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A new approach to the minimum cut problem
Journal of the ACM (JACM)
Approximating s-t minimum cuts in Õ(n2) time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Global min-cuts in RNC, and other ramifications of a simple min-out algorithm
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Experimental study of minimum cut algorithms
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Minimum cuts in near-linear time
Journal of the ACM (JACM)
Trading off space for passes in graph streaming problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On graph problems in a semi-streaming model
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Graph sparsification by effective resistances
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
Streaming algorithms for independent sets
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Intractability of min- and max-cut in streaming graphs
Information Processing Letters
Theory of data stream computing: where to go
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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
Analyzing graph structure via linear measurements
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Graph sketches: sparsification, spanners, and subgraphs
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Streaming graph partitioning for large distributed graphs
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Space-constrained interval selection
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Streaming and communication complexity of clique approximation
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Linear programming in the semi-streaming model with application to the maximum matching problem
Information and Computation
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Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems has been limited. A main reason for this has been the existence of linear space lower bounds for even simple problems such as determining the connectedness of a graph. However, in many new scenarios that arise from social and other interaction networks, the number of vertices is significantly less than the number of edges. This has led to the formulation of the semi-streaming model where we assume that the space is (near) linear in the number of vertices (but not necessarily the edges), and the edges appear in an arbitrary (and possibly adversarial) order. However there has been limited progress in analysing graph algorithms in this model. In this paper we focus on graph sparsification, which is one of the major building blocks in a variety of graph algorithms. Further, there has been a long history of (non-streaming) sampling algorithms that provide sparse graph approximations and it a natural question to ask: since the end result of the sparse approximation is a small (linear) space structure, can we achieve that using a small space, and in addition using a single pass over the data? The question is interesting from the standpoint of both theory and practice and we answer the question in the affirmative, by providing a one pass $\tilde{O}(n/\epsilon^{2})$ space algorithm that produces a sparsification that approximates each cut to a (1 + *** ) factor. We also show that $\Omega(n \log \frac1\epsilon)$ space is necessary for a one pass streaming algorithm to approximate the min-cut, improving upon the *** (n ) lower bound that arises from lower bounds for testing connectivity.