License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2023.84
URN: urn:nbn:de:0030-drops-186180
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Tsai, Meng-Tsung ; Tsai, Shi-Chun ; Wu, Tsung-Ta

Dependent k-Set Packing on Polynomoids

LIPIcs-MFCS-2023-84.pdf (0.7 MB)


Specialized hereditary systems, e.g., matroids, are known to have many applications in algorithm design. We define a new notion called d-polynomoid as a hereditary system (E, ℱ ⊆ 2^E) so that every two maximal sets in ℱ have less than d elements in common. We study the problem that, given a d-polynomoid (E, ℱ), asks if the ground set E contains ? disjoint k-subsets that are not in ℱ, and obtain a complexity trichotomy result for all pairs of k ≥ 1 and d ≥ 0. Our algorithmic result yields a sufficient and necessary condition that decides whether each hypergraph in some classes of r-uniform hypergraphs has a perfect matching, which has a number of algorithmic applications.

BibTeX - Entry

  author =	{Tsai, Meng-Tsung and Tsai, Shi-Chun and Wu, Tsung-Ta},
  title =	{{Dependent k-Set Packing on Polynomoids}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{84:1--84:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-186180},
  doi =		{10.4230/LIPIcs.MFCS.2023.84},
  annote =	{Keywords: Hereditary Systems, Hypergraph Matchings, Compleixty Trichotomy}

Keywords: Hereditary Systems, Hypergraph Matchings, Compleixty Trichotomy
Collection: 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Issue Date: 2023
Date of publication: 21.08.2023

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