M. Cochefert
Parameterized algorithms for finding square roots
Cochefert, M.; Couturier, J-F.; Golovach, P.A.; Paulusma, D.
Authors
Abstract
We show that the following two problems are fixed-parameter tractable with parameter k: testing whether a connected n-vertex graph with m edges has a square root with at most n−1+k edges and testing whether such a graph has a square root with at least m−k edges. Our first result implies that squares of graphs obtained from trees by adding at most k edges can be recognized in polynomial time for every fixed k≥0; previously this result was known only for k=0. Our second result is equivalent to stating that deciding whether a graph can be modified into a square root of itself by at most k edge deletions is fixed-parameter tractable with parameter k.
Citation
Cochefert, M., Couturier, J., Golovach, P., & Paulusma, D. (2014). Parameterized algorithms for finding square roots. Algorithmica, https://doi.org/10.1007/s00453-014-9967-4
Journal Article Type | Article |
---|---|
Publication Date | Dec 1, 2014 |
Deposit Date | Dec 20, 2014 |
Publicly Available Date | Jan 6, 2015 |
Journal | Algorithmica |
Print ISSN | 0178-4617 |
Electronic ISSN | 1432-0541 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
DOI | https://doi.org/10.1007/s00453-014-9967-4 |
Keywords | Parameterized complexity, Graph square root, Generalized kernel |
Public URL | https://durham-repository.worktribe.com/output/1417632 |
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Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-014-9967-4
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