This paper describes efficient algorithms for partitioning a k-edge-connected graph into k edge-disjoint connected subgraphs, each of which has a specified number of elements(vertices and edges). If each subgraph contains the specified element (called base), we call this problem the mixed k-partition problem with bases(called k-PART-WB), otherwise we call it the mixed k-partition problem without bases (called k-PART-WOB). In this paper, we show that k-PART-WB always has a solution for every k-edge-connected graph and we consider the problem without bases and we obtain the following results: (1)for any k≥2, k-PART-WOB can be solved in O(|V|√|V|log2|V|+|E|) time for every 4-edge-connected graph G=(V,E), (2)3-PART-WOB can be solved in O(|V|2) for every 2-edge-connected graph G=(V,E) and (3)4-PART-WOB can be solved in O(|E|2) for every 3-edge-connected graph G=(V,E).
CITATION STYLE
Wada, K., Takaki, A., & Kawaguchi, K. (1995). Efficient algorithms for a mixed k-partition problem of graphs without specifying bases. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 903, pp. 319–330). Springer Verlag. https://doi.org/10.1007/3-540-59071-4_58
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