Graph Mining on Streams

McGregor, Andrew

doi:10.1007/978-0-387-39940-9_184

Cited by 18 publications

(11 citation statements)

References 14 publications

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“…The greedy algorithm to find a maximal matching (simply store every edge that links two currently unmatched nodes) can also be shown to be a 0.5-approximation to the maximum cardinality matching [15]. By taking multiple passes over the input streams, this can be improved to a 1 − approximation, by finding augmenting paths with successive passes [25,26].…”

Section: Related Workmentioning

confidence: 99%

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

Indyk

2014

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As graphs continue to grow in size, we seek ways to effectively process such data at scale. The model of streaming graph processing, in which a compact summary is maintained as each edge insertion/deletion is observed, is an attractive one. However, few results are known for optimization problems over such dynamic graph streams. In this paper, we introduce a new approach to handling graph streams, by instead seeking solutions for the parameterized versions of these problems. Here, we are given a parameter k and the objective is to decide whether there is a solution bounded by k. By combining kernelization techniques with randomized sketch structures, we obtain the first streaming algorithms for the parameterized versions of Maximal Matching and Vertex Cover. We consider various models for a graph stream on n nodes: the insertion-only model where the edges can only be added, and the dynamic model where edges can be both inserted and deleted. More formally, we show the following results: • In the insertion only model, there is a one-pass deterministic algorithm for the parameterized Vertex Cover problem which computes a sketch using

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Section: Related Workmentioning

confidence: 99%

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

Indyk

2014

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“…There exists at least one valid helper h with respect to P and 2. For all helpers h ′ and all streams A, either h ′ is valid for A or h ′ is 1 3 -invalid for A. Conceptually, P is a valid protocol for f if for each stream A there is at least one way to convince V of the true value of f (A), and V rejects all other annotations as invalid (this differs slightly from [6] to allow for multiple h's that can convince V).…”

Section: Model and Definitionsmentioning

confidence: 99%

“…Conceptually, P is a valid protocol for f if for each stream A there is at least one way to convince V of the true value of f (A), and V rejects all other annotations as invalid (this differs slightly from [6] to allow for multiple h's that can convince V). The constant 1 3 can be any constant less than 1 2 . Let h be a valid helper chosen to minimize the length of h(A) for all A.…”

Section: Model and Definitionsmentioning

confidence: 99%

“…This has sparked the study of graph algorithms that meet the constraints of the standard streaming model: restricted memory and the ability to make only one pass (or few passes) over adversarially ordered data. However, many results for graph streams have been negative, as many foundational problems require either substantial working memory or a prohibitive number of passes over the data [1]. Apparently most graph algorithms fundamentally require flexibility in the way they query edges, and therefore the combination of adversarial order and limited memory makes many problems intractable.…”

Section: Introductionmentioning

confidence: 99%

“…To circumvent these negative results, variants and relaxations of the standard graph streaming model have been proposed, including the Semi-Streaming [2], W-Stream [3], Sort-Stream [4], Random-Order [1], and Best-Order [5] models. In Semi-Streaming, memory requirements are relaxed, allowing space proportional to the number of vertices in the stream but not the number provides a feasible solution to the problem.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Streaming Graph Computations with a Helpful Advisor

Cormode

Mitzenmacher

Thaler

2010

Algorithms – ESA 2010

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Motivated by the trend to outsource work to commercial cloud computing services, we consider a variation of the streaming paradigm where a streaming algorithm can be assisted by a powerful helper that can provide annotations to the data stream. We extend previous work on such annotation models by considering a number of graph streaming problems. Without annotations, streaming algorithms for graph problems generally require significant memory; we show that for many standard problems, including all graph problems that can be expressed with totally unimodular integer programming formulations, only a constant number of hash values are needed for single-pass algorithms given linear-sized annotations. We also obtain a protocol achieving optimal tradeoffs between annotation length and memory usage for matrix-vector multiplication; this result contributes to a trend of recent research on numerical linear algebra in streaming models.

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