We consider a partitioning problem for grid graphs with special constraints: a (square) grid graph as well as a number of colors is given, a solution is a coloring approximatively assigning the same number of vertices to each color and such that the induced subgraph for each color is connected. In a "rooted" variant, a vertex to be included in the coloring for each color is specified as well. This problem has a concrete motivation in multimedia streaming applications. We show that the general problem is NP-complete. On the other hand, we define a reasonable easy subclass of grid graphs for which solutions always exist and can be computed by a greedy algorithm.
@InProceedings{berenger_et_al:LIPIcs.MFCS.2018.39, author = {Berenger, Cedric and Niebert, Peter and Perrot, Kevin}, title = {{Balanced Connected Partitioning of Unweighted Grid Graphs}}, booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, pages = {39:1--39:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-086-6}, ISSN = {1868-8969}, year = {2018}, volume = {117}, editor = {Potapov, Igor and Spirakis, Paul and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.39}, URN = {urn:nbn:de:0030-drops-96213}, doi = {10.4230/LIPIcs.MFCS.2018.39}, annote = {Keywords: grid graphs, connected partitioning, NP-completeness, graph algorithm} }
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