Abstract
We introduce a new type of distributed reconfiguration problem, where an initial instance of a combinatorial object is transformed to a goal instance by “local” exchange operations. We present a distributed algorithm that transforms an arbitrary spanning tree to another one through a sequence of spanning trees. We then discuss distributed reconfiguration of hypertrees and maximum bipartite matchings.
This work was supported by JSPS KAKENHI Grant Numbers JP20H05793, JP20H05795, JP18H04091, JP18K11168, JP18K11169, and JP21K11752. The authors would like to thank Shuji Kijima for helpful discussions.
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Notes
- 1.
An orientation of a tree can be obtained in \(\mathrm {O}(n)\) rounds by a tree orientation algorithm [5]. When an initial and a goal spanning trees are not oriented, the proposed algorithm together with the orientation algorithm terminates in \(\mathrm {O}(n)\) rounds.
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Yamauchi, Y., Kamiyama, N., Otachi, Y. (2021). Distributed Reconfiguration of Spanning Trees. In: Johnen, C., Schiller, E.M., Schmid, S. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2021. Lecture Notes in Computer Science(), vol 13046. Springer, Cham. https://doi.org/10.1007/978-3-030-91081-5_40
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DOI: https://doi.org/10.1007/978-3-030-91081-5_40
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