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The complexity of approximately counting retractions to square-free graphs

Abstract:
A retraction is a homomorphism from a graph G to an induced subgraph H of G that is the identity on H. In a long line of research, retractions have been studied under various algorithmic settings. Recently, the problem of approximately counting retractions was considered. We give a complete trichotomy for the complexity of approximately counting retractions to all square-free graphs (graphs that do not contain a cycle of length 4). It turns out there is a rich and interesting class of graphs for which this problem is complete in the class #BIS. As retractions generalise homomorphisms, our easiness results extend to the important problem of approximately counting homomorphisms. By giving new #BIS-easiness results, we now settle the complexity of approximately counting homomorphisms for a whole class of non-trivial graphs that were previously unresolved.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1145/3458040

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Computer Science
Role:
Author
ORCID:
0000-0002-0263-159X


Publisher:
Association for Computing Machinery
Journal:
ACM Transactions on Algorithms More from this journal
Volume:
17
Issue:
3
Article number:
22
Publication date:
2021-07-12
Acceptance date:
2021-03-01
DOI:
EISSN:
1549-6333
ISSN:
1549-6325


Language:
English
Keywords:
Pubs id:
1168844
Local pid:
pubs:1168844
Deposit date:
2021-03-20

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