conference paper
On the Complexity of Local Graph Transformations
published
Christian
Scheideler
author 20792
Alexander
Setzer
author 11108
79
department
ICALP 2019
SFB 901
project
SFB 901 - Subproject A1
project
SFB 901 - Project Area A
project
We consider the problem of transforming a given graph G_s into a desired graph G_t by applying a minimum number of primitives from a particular set of local graph transformation primitives. These primitives are local in the sense that each node can apply them based on local knowledge and by affecting only its 1-neighborhood. Although the specific set of primitives we consider makes it possible to transform any (weakly) connected graph into any other (weakly) connected graph consisting of the same nodes, they cannot disconnect the graph or introduce new nodes into the graph, making them ideal in the context of supervised overlay network transformations. We prove that computing a minimum sequence of primitive applications (even centralized) for arbitrary G_s and G_t is NP-hard, which we conjecture to hold for any set of local graph transformation primitives satisfying the aforementioned properties. On the other hand, we show that this problem admits a polynomial time algorithm with a constant approximation ratio.
https://ris.uni-paderborn.de/download/10586/12955/LIPIcs-ICALP-2019-150.pdf
application/pdf
Dagstuhl Publishing2019Patras, Greece
eng
Graphs transformationsNP-hardnessapproximation algorithms
Proceedings of the 46th International Colloquium on Automata, Languages, and Programming10.4230/LIPICS.ICALP.2019.150
132150:1--150:14
C. Scheideler, A. Setzer, in: Proceedings of the 46th International Colloquium on Automata, Languages, and Programming, Dagstuhl Publishing, 2019, pp. 150:1--150:14.
C. Scheideler and A. Setzer, “On the Complexity of Local Graph Transformations,” in <i>Proceedings of the 46th International Colloquium on Automata, Languages, and Programming</i>, Patras, Greece, 2019, vol. 132, pp. 150:1--150:14.
Scheideler C, Setzer A. On the Complexity of Local Graph Transformations. In: <i>Proceedings of the 46th International Colloquium on Automata, Languages, and Programming</i>. Vol 132. LIPIcs. Dagstuhl Publishing; 2019:150:1--150:14. doi:<a href="https://doi.org/10.4230/LIPICS.ICALP.2019.150">10.4230/LIPICS.ICALP.2019.150</a>
Scheideler, Christian, and Alexander Setzer. “On the Complexity of Local Graph Transformations.” In <i>Proceedings of the 46th International Colloquium on Automata, Languages, and Programming</i>, 132:150:1--150:14. LIPIcs. Dagstuhl Publishing, 2019. <a href="https://doi.org/10.4230/LIPICS.ICALP.2019.150">https://doi.org/10.4230/LIPICS.ICALP.2019.150</a>.
@inproceedings{Scheideler_Setzer_2019, series={LIPIcs}, title={On the Complexity of Local Graph Transformations}, volume={132}, DOI={<a href="https://doi.org/10.4230/LIPICS.ICALP.2019.150">10.4230/LIPICS.ICALP.2019.150</a>}, booktitle={Proceedings of the 46th International Colloquium on Automata, Languages, and Programming}, publisher={Dagstuhl Publishing}, author={Scheideler, Christian and Setzer, Alexander}, year={2019}, pages={150:1--150:14}, collection={LIPIcs} }
Scheideler, Christian, and Alexander Setzer. “On the Complexity of Local Graph Transformations.” <i>Proceedings of the 46th International Colloquium on Automata, Languages, and Programming</i>, vol. 132, Dagstuhl Publishing, 2019, pp. 150:1--150:14, doi:<a href="https://doi.org/10.4230/LIPICS.ICALP.2019.150">10.4230/LIPICS.ICALP.2019.150</a>.
Scheideler, C., & Setzer, A. (2019). On the Complexity of Local Graph Transformations. In <i>Proceedings of the 46th International Colloquium on Automata, Languages, and Programming</i> (Vol. 132, pp. 150:1--150:14). Patras, Greece: Dagstuhl Publishing. <a href="https://doi.org/10.4230/LIPICS.ICALP.2019.150">https://doi.org/10.4230/LIPICS.ICALP.2019.150</a>
105862019-07-08T17:19:01Z2022-01-06T06:50:45Z