Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Graph Sketching

  • Andrew McGregor
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_796-1

Years and Authors of Summarized Original Work

  • 2012a; Ahn, Guha, McGregor

Problem Definition

The basic problem we consider is testing whether an undirected graph G on n nodes \(\{v_{1},\ldots ,v_{n}\}\)


Connectivity Data streams Linear projections 
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Recommended Reading

  1. 1.
    Ahn KJ, Guha S, McGregor A (2012) Analyzing graph structure via linear measurements. In: Twenty-third annual ACM-SIAM symposium on discrete algorithms, SODA 2012, pp 459–467. http://portal.acm.org/citation.cfm?id=2095156%26CFID=63838676%26CFTOKEN=79617016
  2. 2.
    Ahn KJ, Guha S, McGregor A (2012) Graph sketches: sparsification, spanners, and subgraphs. In: 31st ACM SIGMOD-SIGACT-SIGART symposium on principles of database systems, pp 5–14. DOI10.1145/2213556.2213560, http://doi.acm.org/10.1145/2213556.2213560
  3. 3.
    Ahn KJ, Guha S, McGregor A (2013) Spectral sparsification in dynamic graph streams. In: APPROX, pp 1–10. DOI10.1007/978-3-642-40328-6_1, http://dx.doi.org/10.1007/978-3-642-40328-6_1
  4. 4.
    Ahn KJ, Cormode G, Guha S, McGregor A, Wirth A (2015) Correlation clustering in data streams. In: ICML, LilleGoogle Scholar
  5. 5.
    Assadi S, Khanna S, Li Y, Yaroslavtsev G (2015) Tight bounds for linear sketches of approximate matchings. CoRR abs/1505.01467. http://arxiv.org/abs/1505.01467
  6. 6.
    Bhattacharya S, Henzinger M, Nanongkai D, Tsourakakis CE (2015) Space- and time-efficient algorithm for maintaining dense subgraphs on one-pass dynamic streams. In: STOC, PortlandGoogle Scholar
  7. 7.
    Bury M, Schwiegelshohn C (2015) Sublinear estimation of weighted matchings in dynamic data streams. CoRR abs/1505.02019. http://arxiv.org/abs/1505.02019
  8. 8.
    Chitnis RH, Cormode G, Esfandiari H, Hajiaghayi M, McGregor A, Monemizadeh M, Vorotnikova S (2015) Kernelization via sampling with applications to dynamic graph streams. CoRR abs/1505.01731. http://arxiv.org/abs/1505.01731
  9. 9.
    Esfandiari H, Hajiaghayi M, Woodruff DP (2015) Applications of uniform sampling: densest subgraph and beyond. CoRR abs/1506.04505. http://arxiv.org/abs/1506.04505
  10. 10.
    Goel A, Kapralov M, Post I (2012) Single pass sparsification in the streaming model with edge deletions. CoRR abs/1203.4900. http://arxiv.org/abs/1203.4900
  11. 11.
    Guha S, McGregor A, Tench D (2015) Vertex and hypergraph connectivity in dynamic graph streams. In: PODS, MelbourneGoogle Scholar
  12. 12.
    Jowhari H, Saglam M, Tardos G (2011) Tight bounds for lp samplers, finding duplicates in streams, and related problems. In: PODS, Athens, pp 49–58Google Scholar
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    Kapralov M, Woodruff DP (2014) Spanners and sparsifiers in dynamic streams. In: ACM symposium on principles of distributed computing, PODC ’14, Paris, 15–18 July 2014, pp 272–281. DOI10.1145/2611462.2611497, http://doi.acm.org/10.1145/2611462.2611497
  14. 14.
    Kapralov M, Lee YT, Musco C, Musco C, Sidford A (2014) Single pass spectral sparsification in dynamic streams. In: FOCS, PhiladelphiaGoogle Scholar
  15. 15.
    Kapron B, King V, Mountjoy (2013) Dynamic graph connectivity in polylogarithmic worst case time. In: SODA, New Orleans, pp 1131–1142Google Scholar
  16. 16.
    Konrad C (2015) Maximum matching in turnstile streams. CoRR abs/1505.01460. http://arxiv.org/abs/1505.01460
  17. 17.
    Kutzkov K, Pagh R (2014) Triangle counting in dynamic graph streams. In: Algorithm theory – SWAT 2014 – 14th Scandinavian symposium and workshops, proceedings, Copenhagen, 2–4 July 2014, pp 306–318. DOI10.1007/978-3-319-08404-6_27, http://dx.doi.org/10.1007/978-3-319-08404-6_27
  18. 18.
    McGregor A, Tench D, Vorotnikova S, Vu H (2015) Densest subgraph in dynamic graph streams. In: Mathematical foundations of computer science 2015 – 40th international symposium, MFCS 2014, Proceedings, Part I, Milano, 24–28 Aug 2014Google Scholar
  19. 19.
    Sun X, Woodruff D (2015) Tight bounds for graph problems in insertion streams. In: Approximation algorithms for combinatorial optimization, eighteenth international workshop, APPROX 2015, Proceedings, Princeton, 24–26 Aug 2015Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of MassachusettsAmherst, MAUSA