DROPS

Document

DOI: 10.4230/LIPIcs.MFCS.2023.84

Dependent k-Set Packing on Polynomoids

Authors: Meng-Tsung Tsai, Shi-Chun Tsai, and Tsung-Ta Wu

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract

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 𝓁 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.

Cite as

Meng-Tsung Tsai, Shi-Chun Tsai, and Tsung-Ta Wu. Dependent k-Set Packing on Polynomoids. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 84:1-84:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{tsai_et_al:LIPIcs.MFCS.2023.84,
  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 =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.84},
  URN =		{urn:nbn:de:0030-drops-186180},
  doi =		{10.4230/LIPIcs.MFCS.2023.84},
  annote =	{Keywords: Hereditary Systems, Hypergraph Matchings, Compleixty Trichotomy}
}

Search Results

Documents authored by Wu, Tsung-Ta

Dependent k-Set Packing on Polynomoids

Abstract

Cite as

Thanks for your feedback!

Could not send message