TY - GEN
T1 - Reconfiguration of Spanning Trees with Degree Constraint or Diameter Constraint
AU - Bousquet, Nicolas
AU - Kobayashi, Yusuke
AU - Ouvrard, Paul
AU - Wasa, Kunihiro
AU - Ito, Takehiro
AU - Mizuta, Haruka
AU - Suzuki, Akira
N1 - Funding Information:
Funding This work is partially supported by JSPS and MEAE-MESRI under the Japan-France Integrated Action Program (SAKURA). Nicolas Bousquet: This work was supported by ANR project GrR (ANR-18-CE40-0032). Takehiro Ito: Partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP19K11814 and JP20H05793, Japan. Yusuke Kobayashi: Partially supported by JSPS KAKENHI Grant Numbers 18H05291, JP20K11692, and 20H05795, Japan. Paul Ouvrard: This work was supported by ANR project GrR (ANR-18-CE40-0032). Akira Suzuki: Partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP20K11666 and JP20H05794, Japan. Kunihiro Wasa: Partially supported by JST CREST Grant Numbers JPMJCR18K3 and JP-MJCR1401, and JSPS KAKENHI Grant Numbers 19K20350 and JP20H05793, Japan.
Publisher Copyright:
© Nicolas Bousquet, Takehiro Ito, Yusuke Kobayashi, Haruka Mizuta, Paul Ouvrard, Akira Suzuki and Kunihiro Wasa.
PY - 2022/3/1
Y1 - 2022/3/1
N2 - We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases immediately yields that such a transformation always exists if we have no constraints on spanning trees. In this paper, we wish to find a transformation which passes through only spanning trees satisfying some constraint. Our focus is bounding either the maximum degree or the diameter of spanning trees, and we give the following results. The problem with a lower bound on maximum degree is solvable in polynomial time, while the problem with an upper bound on maximum degree is PSPACE-complete. The problem with a lower bound on diameter is NP-hard, while the problem with an upper bound on diameter is solvable in polynomial time.
AB - We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases immediately yields that such a transformation always exists if we have no constraints on spanning trees. In this paper, we wish to find a transformation which passes through only spanning trees satisfying some constraint. Our focus is bounding either the maximum degree or the diameter of spanning trees, and we give the following results. The problem with a lower bound on maximum degree is solvable in polynomial time, while the problem with an upper bound on maximum degree is PSPACE-complete. The problem with a lower bound on diameter is NP-hard, while the problem with an upper bound on diameter is solvable in polynomial time.
KW - Algorithms
KW - Combinatorial reconfiguration
KW - PSPACE
KW - Polynomial-time
KW - Spanning trees
UR - http://www.scopus.com/inward/record.url?scp=85127203518&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85127203518&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.STACS.2022.15
DO - 10.4230/LIPIcs.STACS.2022.15
M3 - Conference contribution
AN - SCOPUS:85127203518
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022
A2 - Berenbrink, Petra
A2 - Monmege, Benjamin
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022
Y2 - 15 May 2022 through 18 May 2022
ER -