Document Open Access Logo

Fractional Covers of Hypergraphs with Bounded Multi-Intersection

Authors Georg Gottlob, Matthias Lanzinger, Reinhard Pichler, Igor Razgon

PDF

File

Thumbnail PDF
PDF
LIPIcs.MFCS.2020.41.pdf
  • Filesize: 493 kB
  • 14 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Hypergraphs
  • Mathematics of computing → Enumeration
  • Information systems → Relational database query languages
Keywords
  • Fractional graph theory
  • fractional edge cover
  • fractional hypertree width
  • bounded multi-intersection
  • fractional cover
  • fractional vertex cover

Metrics

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

Abstract

Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of hypergraphs. Our main technical result generalizes and unifies previous conditions under which the size of the support of fractional edge covers is bounded independently of the size of the hypergraph itself. This allows us to extend previous tractability results for checking if the fractional hypertree width of a given hypergraph is ≤ k for some constant k. We also show how our results translate to fractional vertex covers.

Cite As Get BibTex

Georg Gottlob, Matthias Lanzinger, Reinhard Pichler, and Igor Razgon. Fractional Covers of Hypergraphs with Bounded Multi-Intersection. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 41:1-41:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.MFCS.2020.41

Author Details

Georg Gottlob
  • University of Oxford, UK
  • TU Wien, Austria
Matthias Lanzinger
  • TU Wien, Austria
Reinhard Pichler
  • TU Wien, Austria
Igor Razgon
  • Birkbeck University of London, UK

Funding

This work was supported by the Austrian Science Fund (FWF):P30930.
  • Gottlob, Georg: Work supported by the Royal Society Research Professorship grant "RAISON DATA" (Project reference: RP\R1\201074).

References

  1. Albert Atserias, Martin Grohe, and Dániel Marx. Size bounds and query plans for relational joins. SIAM J. Comput., 42(4):1737-1767, 2013. URL: https://doi.org/10.1137/110859440.
  2. Claude Berge. Fractional Graph Theory. ISI Lecture Notes 1, Macmillan of India, 1978. Google Scholar
  3. Fan R. K. Chung, Zoltán Füredi, M. R. Garey, and Ronald L. Graham. On the fractional covering number of hypergraphs. SIAM J. Discret. Math., 1(1):45-49, 1988. URL: https://doi.org/10.1137/0401005.
  4. Wolfgang Fischl, Georg Gottlob, Davide Mario Longo, and Reinhard Pichler. Hyperbench: A benchmark and tool for hypergraphs and empirical findings. In Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2019, Amsterdam, The Netherlands, June 30 - July 5, 2019, pages 464-480, 2019. URL: https://doi.org/10.1145/3294052.3319683.
  5. Wolfgang Fischl, Georg Gottlob, and Reinhard Pichler. General and fractional hypertree decompositions: Hard and easy cases. In Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2020, Houston, TX, USA, June 10-15, 2018, pages 17-32, 2018. URL: https://doi.org/10.1145/3196959.3196962.
  6. Zoltán Füredi. Matchings and covers in hypergraphs. Graphs Comb., 4(1):115-206, 1988. URL: https://doi.org/10.1007/BF01864160.
  7. Georg Gottlob, Matthias Lanzinger, Reinhard Pichler, and Igor Razgon. Complexity analysis of generalized and fractional hypertree decompositions. CoRR, abs/2002.05239, 2020. URL: http://arxiv.org/abs/2002.05239.
  8. Georg Gottlob, Matthias Lanzinger, Reinhard Pichler, and Igor Razgon. Fractional covers of hypergraphs with bounded multi-intersection. CoRR, abs/2007.01830, 2020. URL: http://arxiv.org/abs/2007.01830.
  9. Martin Grohe and Dániel Marx. Constraint solving via fractional edge covers. ACM Trans. Algorithms, 11(1):4:1-4:20, 2014. URL: https://doi.org/10.1145/2636918.
  10. Geevarghese Philip, Venkatesh Raman, and Somnath Sikdar. Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond. ACM Trans. Algorithms, 9(1):11:1-11:23, 2012. URL: https://doi.org/10.1145/2390176.2390187.
  11. Edward Scheinerman and Daniel Ullman. Fractional Graph Theory: A Rational Approach to the Theory of Graphs. Dover Publications, Inc., 2011. Google Scholar
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