Generating All Patterns of Graph Partitions Within a Disparity Bound
A balanced graph partition on a vertex-weighted graph is a partition of the vertex set such that the partition has k parts and the disparity, which is defined as the ratio of the maximum total weight of parts to the minimum one, is at most r. In this paper, a novel algorithm is proposed that enumerates all the graph partitions with small disparity. Experimental results show that five millions of partitions with small disparity for some graph with more than 100 edges can be enumerated within ten minutes.
The authors would like to thank Dr. Toshiki Saitoh, Dr. Norihito Yasuda and Dr. Ryo Yoshinaka for their valuable comments. This work was partly supported by JSPS KAKENHI 15H05711, 24106007 and 15K00008.
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