Years and Authors of Summarized Original Work
1997, 2014; Cohen
2002; Palmer, Gibbons, Faloutsos
2004, 2007; Cohen, Kaplan
Problem Definition
All-distances sketches (The term least element lists was used in [3]; the terms MV/D lists and Neighborhood summaries were used in [6].) are randomized summary structures of the distance relations of nodes in a graph. The graph can be directed or undirected, and edges can have uniform or general nonnegative weights.
Preprocessing Cost
A set of sketches, \(\mathop{\mathrm{ADS}}(v)\) for each node v, can be computed efficiently, using a near-linear number of edge traversals. The sketch sizes are well concentrated, with logarithmic dependence on the total number of nodes.
Supported Queries
The sketches support approximate distance-based queries, which include:
Distance distribution: The query specifies a node v and value d ≥ 0 and returns the cardinality | N d (v) | of the d-neighborhood of vN d (v) = { u∣d vu  ≤ d}, where d uv...
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Recommended Reading
Boldi P, Vigna S (2014) Axioms for centrality. Internet Math 10:222–262
Boldi P, Rosa M, Vigna S (2011) HyperANF: approximating the neighbourhood function of very large graphs on a budget. In: WWW, Hyderabad
Cohen E (1997) Size-estimation framework with applications to transitive closure and reachability. J Comput Syst Sci 55:441–453
Cohen E (2014) All-distances sketches, revisited: HIP estimators for massive graphs analysis. In: PODS. ACM. http://arxiv.org/abs/1306.3284
Cohen E (2014) Estimation for monotone sampling: competitiveness and customization. In: PODC. ACM. http://arxiv.org/abs/1212.0243, full version http://arxiv.org/abs/1212.0243
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Cohen, E. (2016). All-Distances Sketches. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_574
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