Document Open Access Logo

Sparsification of Binary CSPs

Authors Silvia Butti , Stanislav Živný

PDF

File

Thumbnail PDF
PDF
LIPIcs.STACS.2019.17.pdf
  • Filesize: 427 kB
  • 8 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • constraint satisfaction problems
  • minimum cuts
  • sparsification

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

A cut epsilon-sparsifier of a weighted graph G is a re-weighted subgraph of G of (quasi)linear size that preserves the size of all cuts up to a multiplicative factor of epsilon. Since their introduction by Benczúr and Karger [STOC'96], cut sparsifiers have proved extremely influential and found various applications. Going beyond cut sparsifiers, Filtser and Krauthgamer [SIDMA'17] gave a precise classification of which binary Boolean CSPs are sparsifiable. In this paper, we extend their result to binary CSPs on arbitrary finite domains.

Cite As Get BibTex

Silvia Butti and Stanislav Živný. Sparsification of Binary CSPs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 17:1-17:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.STACS.2019.17

Author Details

Silvia Butti
  • Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
Stanislav Živný
  • Department of Computer Science, University of Oxford, UK

Funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714532). The paper reflects only the authors' views and not the views of the ERC or the European Commission. The European Union is not liable for any use that may be made of the information contained therein.
  • Butti, Silvia: Work mostly done while at the University of Oxford.
  • Živný, Stanislav: Stanislav Živný was supported by a Royal Society University Research Fellowship.

References

  1. Kook Jin Ahn and Sudipto Guha. Graph Sparsification in the Semi-streaming Model. In Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP'09), Part II, volume 5556 of Lecture Notes in Computer Science, pages 328-338. Springer, 2009. URL: http://dx.doi.org/10.1007/978-3-642-02930-1_27.
  2. Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. On Sketching Quadratic Forms. In Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science (ITCS'16), pages 311-319, 2016. URL: http://dx.doi.org/10.1145/2840728.2840753.
  3. Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. Twice-Ramanujan Sparsifiers. SIAM Journal on Computing, 41(6):1704-1721, 2012. URL: http://dx.doi.org/10.1137/090772873.
  4. András A. Benczúr and David R. Karger. Approximating s-t Minimum Cuts in Õ(n^2) Time. In Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing (STOC'96), pages 47-55, 1996. URL: http://dx.doi.org/10.1145/237814.237827.
  5. Richard A. Brualdi, Frank Harary, and Zevi Miller. Bigraphs versus digraphs via matrices. Journal of Graph Theory, 4(1):51-73, 1980. URL: http://dx.doi.org/10.1002/jgt.3190040107.
  6. Hubie Chen, Bart M. P. Jansen, and Astrid Pieterse. Best-case and Worst-case Sparsifiability of Boolean CSPs. In Proceedings of the 13th International Symposium on Parameterized and Exact Computation (IPEC'18), 2018. URL: http://arxiv.org/abs/1809.06171.
  7. Arnold Filtser and Robert Krauthgamer. Sparsification of Two-Variable Valued Constraint Satisfaction Problems. SIAM Journal on Discrete Mathematics, 31(2):1263-1276, 2017. URL: http://dx.doi.org/10.1137/15M1046186.
  8. Wai Shing Fung, Ramesh Hariharan, Nicholas J. A. Harvey, and Debmalya Panigrahi. A general framework for graph sparsification. In Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC'11), pages 71-80. ACM, 2011. URL: http://dx.doi.org/10.1145/1993636.1993647.
  9. Dmitry Kogan and Robert Krauthgamer. Sketching Cuts in Graphs and Hypergraphs. In Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science (ITCS'15), pages 367-376, 2015. URL: http://dx.doi.org/10.1145/2688073.2688093.
  10. Vladimir Kolmogorov, Andrei A. Krokhin, and Michal Rolínek. The Complexity of General-Valued CSPs. SIAM Journal on Computing, 46(3):1087-1110, 2017. URL: http://dx.doi.org/10.1137/16M1091836.
  11. Ilan Newman and Yuri Rabinovich. On Multiplicative Lambda-Approximations and Some Geometric Applications. SIAM Journal on Computing, 42(3):855-883, 2013. URL: http://dx.doi.org/10.1137/100801809.
  12. Tasuko Soma and Yuichi Yoshida. Spectral Sparsification of Hypergraphs. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'19), 2019. Google Scholar
  13. Daniel A. Spielman and Nikhil Srivastava. Graph Sparsification by Effective Resistances. SIAM Journal on Computing, 40(6):1913-1926, 2011. URL: http://dx.doi.org/10.1137/080734029.
  14. Daniel A. Spielman and Shang-Hua Teng. Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC'04), pages 81-90. ACM, 2004. URL: http://dx.doi.org/10.1145/1007352.1007372.
  15. Daniel A. Spielman and Shang-Hua Teng. Spectral Sparsification of Graphs. SIAM Journal on Computing, 40(4):981-1025, 2011. URL: http://dx.doi.org/10.1137/08074489X.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact