Academic Journal
Parameterized Complexities of Dominating and Independent Set Reconfiguration
| Title: | Parameterized Complexities of Dominating and Independent Set Reconfiguration |
|---|---|
| Authors: | Bodlaender, Hans L., Groenland, Carla, Swennenhuis, Céline M. F. |
| Contributors: | Hans L. Bodlaender and Carla Groenland and Céline M. F. Swennenhuis, Sub Algorithms and Complexity, Algorithms and Complexity, Golovach, Petr A., Zehavi, Meirav |
| Publication Status: | Preprint |
| Publisher Information: | Research Square Platform LLC, 2022. |
| Publication Year: | 2022 |
| Subject Terms: | FOS: Computer and information sciences, Theory of computation → Problems, reductions and completeness, Dominating set reconfiguration, XNL, 0102 computer and information sciences, 02 engineering and technology, Computational Complexity (cs.CC), 01 natural sciences, dominating set reconfiguration, Parameterized complexity, Computer Science - Computational Complexity, independent set reconfiguration, 0202 electrical engineering, electronic engineering, information engineering, Theory of computation → Parameterized complexity and exact algorithms, XL, XNLP, ddc:004, Independent set reconfiguration, W-hierarchy, 68Q27, 68Q25, Software |
| Description: | We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on the number of moves, XNL-complete when a maximum length l for the sequence is given in binary in the input, and XNLP-complete when l is given in unary. The problems were known to be W[1]- and W[2]-hard respectively when l is also a parameter. We complete the picture by showing membership in those classes. Moreover, we show that for all the variants that we consider, token sliding and token jumping are equivalent under pl-reductions. We introduce partitioned variants of token jumping and token sliding, and give pl-reductions between the four variants that have precise control over the number of tokens and the length of the reconfiguration sequence. |
| Document Type: | Article Conference object Part of book or chapter of book |
| File Description: | application/pdf |
| DOI: | 10.21203/rs.3.rs-2049659/v1 |
| DOI: | 10.48550/arxiv.2106.15907 |
| DOI: | 10.4230/lipics.ipec.2021.9 |
| Access URL: | http://arxiv.org/abs/2106.15907 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.9 https://dspace.library.uu.nl/handle/1874/416476 |
| Rights: | CC BY CC BY NC ND |
| Accession Number: | edsair.doi.dedup.....1a739453856b51ee371bbaa4eb1f0fd0 |
| Database: | OpenAIRE |
| DOI: | 10.21203/rs.3.rs-2049659/v1 |
|---|