2026-08-05T06:20:28Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17692 2024-03-06T11:00:19Z ddc:004 open_access

Finding and Counting Patterns in Sparse Graphs Komarath, Balagopal Kumar, Anant Mishra, Suchismita Sethia, Aditi Subgraph Detection and Counting Homomorphism Polynomials Treewidth and Treedepth Matchings 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Balagopal Komarath and Anant Kumar and Suchismita Mishra and Aditi Sethia 2023 Is Part Of LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2023.40 urn:nbn:de:0030-drops-176921 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.40 eng https://creativecommons.org/licenses/by/4.0/legalcode