Complexity and algorithms for constant diameter augmentation problems
•For given integers d, k and graph G, can we obtain a graph with diameter d via at most k edge deletions?•We determine the computational complexity of this and related problems for different values of d.•For d=3, the problem is related to Moore graphs and solvable in polynomial time.•For all d>4,...
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| Veröffentlicht in: | Theoretical computer science Jg. 904; S. 15 - 26 |
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15.02.2022
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | •For given integers d, k and graph G, can we obtain a graph with diameter d via at most k edge deletions?•We determine the computational complexity of this and related problems for different values of d.•For d=3, the problem is related to Moore graphs and solvable in polynomial time.•For all d>4, the problem is NP-complete.•The NP-completeness results are proved for various values of the diameter of the input graph.
We study the following problem: for given integers d,k and graph G, can we obtain a graph with diameter d via at most k edge deletions? We determine the computational complexity of this and related problems for different values of d. |
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| AbstractList | •For given integers d, k and graph G, can we obtain a graph with diameter d via at most k edge deletions?•We determine the computational complexity of this and related problems for different values of d.•For d=3, the problem is related to Moore graphs and solvable in polynomial time.•For all d>4, the problem is NP-complete.•The NP-completeness results are proved for various values of the diameter of the input graph.
We study the following problem: for given integers d,k and graph G, can we obtain a graph with diameter d via at most k edge deletions? We determine the computational complexity of this and related problems for different values of d. |
| Author | Monnot, Jérôme Kim, Eun Jung Picouleau, Christophe Milanič, Martin |
| Author_xml | – sequence: 1 givenname: Eun Jung surname: Kim fullname: Kim, Eun Jung email: eunjungkim78@gmail.com organization: Université Paris-Dauphine, Paris, France – sequence: 2 givenname: Martin orcidid: 0000-0002-8222-8097 surname: Milanič fullname: Milanič, Martin email: martin.milanic@upr.si organization: FAMNIT and IAM, University of Primorska, Koper, Slovenia – sequence: 3 givenname: Jérôme surname: Monnot fullname: Monnot, Jérôme organization: Université Paris-Dauphine, Paris, France – sequence: 4 givenname: Christophe surname: Picouleau fullname: Picouleau, Christophe email: christophe.picouleau@cnam.fr organization: Conservatoire National des Arts et Métiers, CEDRIC laboratory, Paris, France |
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| Cites_doi | 10.1007/s00453-014-9886-4 10.1016/j.disc.2009.08.009 10.1016/0166-218X(92)90126-U 10.1016/j.disc.2018.03.024 10.1016/S0021-9800(68)80030-4 10.2307/2315106 10.1007/s00224-007-9025-6 10.1016/j.tcs.2018.06.023 10.1016/j.disc.2009.01.006 10.1002/net.21556 10.1016/j.disopt.2005.10.006 10.1007/s00373-013-1380-2 10.1016/j.laa.2018.12.035 10.1016/j.ejor.2015.05.037 10.1002/jgt.3190110315 10.1016/j.dam.2013.01.016 10.1145/1868237.1868241 10.1016/0167-6377(92)90007-P 10.1137/130907392 10.1016/j.dam.2011.06.023 10.1002/jgt.3190080408 10.1007/s10878-010-9334-6 10.1016/j.jctb.2015.11.004 10.1016/0022-0000(80)90060-4 10.1007/s10107-010-0366-6 10.1016/0166-218X(83)90101-4 |
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| SubjectTerms | Blocker problem Graph diameter NP-complete Polynomial algorithm |
| Title | Complexity and algorithms for constant diameter augmentation problems |
| URI | https://dx.doi.org/10.1016/j.tcs.2021.05.020 |
| Volume | 904 |
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