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.STACS.2023.40
URN: urn:nbn:de:0030-drops-176921
URL: https://drops.dagstuhl.de/opus/volltexte/2023/17692/
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Komarath, Balagopal ; Kumar, Anant ; Mishra, Suchismita ; Sethia, Aditi

Finding and Counting Patterns in Sparse Graphs

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LIPIcs-STACS-2023-40.pdf (0.7 MB)

Abstract

We consider algorithms for finding and counting small, fixed graphs in sparse host graphs. In the non-sparse setting, the parameters treedepth and treewidth play a crucial role in fast, constant-space and polynomial-space algorithms respectively. We discover two new parameters that we call matched treedepth and matched treewidth. We show that finding and counting patterns with low matched treedepth and low matched treewidth can be done asymptotically faster than the existing algorithms when the host graphs are sparse for many patterns. As an application to finding and counting fixed-size patterns, we discover Õ(m³)-time, constant-space algorithms for cycles of length at most 11 and Õ(m²)-time, polynomial-space algorithms for paths of length at most 10.

BibTeX - Entry

@InProceedings{komarath_et_al:LIPIcs.STACS.2023.40,
  author =	{Komarath, Balagopal and Kumar, Anant and Mishra, Suchismita and Sethia, Aditi},
  title =	{{Finding and Counting Patterns in Sparse Graphs}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{40:1--40:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17692},
  URN =		{urn:nbn:de:0030-drops-176921},
  doi =		{10.4230/LIPIcs.STACS.2023.40},
  annote =	{Keywords: Subgraph Detection and Counting, Homomorphism Polynomials, Treewidth and Treedepth, Matchings}
}

Keywords: Subgraph Detection and Counting, Homomorphism Polynomials, Treewidth and Treedepth, Matchings
Collection: 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)
Issue Date: 2023
Date of publication: 03.03.2023
Supplementary Material: Dataset (Graphs): https://github.com/anonymous1203/Spasm

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