Approximating the independent domatic partition problem in random geometric graphs - an experimental study
نویسندگان
چکیده
We investigate experimentally the Domatic Partition (DP) problem, the Independent Domatic Partition (IDP) problem and the Idomatic partition problem in Random Geometric Graphs (RGGs). In particular, we model these problems as Integer Linear Programs (ILPs), solve them optimally, and show on a large set of samples that RGGs are independent domatically full most likely (over 93% of the cases) and domatically full almost certainly (100% of the cases). We empirically confirm using two methods that RGGs are not idomatic on any of the samples. We compare the results of the ILP-based exact algorithms with those of known coloring algorithms both centralized and distributed. Coloring algorithms achieve a competitive performance ratio in solving the IDP problem [11, 10]. Our results on the high likelihood of the “independent domatic fullness” of RGGs lead us to believe that coloring algorithms can be specifically enhanced to achieve a better performance ratio on the IDP size than [11, 10]. We also investigate experimentally the extremal sizes of individual dominating and independent sets of the partitions.
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