LIPIcs.MFCS.2020.41.pdf
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Fractional Covers of Hypergraphs with Bounded Multi-Intersection
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45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Mathematical Foundations of Computer Science (MFCS) - License:
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- Publication Date: 2020-08-18
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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
https://doi.org/10.4230/LIPIcs.MFCS.2020.41
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.
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
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References
- 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.
-
Claude Berge. Fractional Graph Theory. ISI Lecture Notes 1, Macmillan of India, 1978.
- 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.
- 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.
- 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.
- Zoltán Füredi. Matchings and covers in hypergraphs. Graphs Comb., 4(1):115-206, 1988. URL: https://doi.org/10.1007/BF01864160.
- 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.
- 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.
- 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.
- 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.
-
Edward Scheinerman and Daniel Ullman. Fractional Graph Theory: A Rational Approach to the Theory of Graphs. Dover Publications, Inc., 2011.