Partitioning a Multi-Weighted Graph to Connected Subgraphs of Almost Uniform Size

T. ITO, K. GOTO, X. ZHOU, T. NISHIZEKI
2007 IEICE transactions on information and systems  
Assume that each vertex of a graph G is assigned a constant number q of nonnegative integer weights, and that q pairs of nonnegative integers li and ui, 1 ≤ i ≤ q, are given. One wishes to partition G into connected components by deleting edges from G so that the total i-th weights of all vertices in each component is at least li and at most ui for each index i, 1 ≤ i ≤ q. The problem of finding such a "uniform" partition is NP-hard for series-parallel graphs, and is strongly NP-hard for
more » ... graphs even for q = 1. In this paper we show that the problem and many variants can be solved in pseudo-polynomial time for seriesparallel graphs. Our algorithms for series-parallel graphs can be extended for partial k-trees, that is, graphs with bounded tree-width.
doi:10.1093/ietisy/e90-d.2.449 fatcat:xwdaiidgcveonkvixcgu7ej52q