Abstract
Given a setX and subsetsX 1,...,X m, we consider the problem of finding a graphG with vertex setX and the minimum number of edges such that fori=1,...,m, the subgraphG i; induced byX i is connected. Suppose that for anyα pointsx 1,...,x α ε X, there are at mostβX i 's containing the set {x1,...,x α}. In the paper, we show that the problem is polynomial-time solvable for (α ⩽ 2,β ⩽ 2) and is NP-hard for (α⩾3,β=1), (α=l,β⩾6), and (α⩾2,β⩾3).
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Support in part by the NSF under grant CCR-9208913 and CCR-8920505.
Part work was done while this author was visiting at DIMACS and on leave from Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing.
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Du, D.Z., Kelley, D.F. On complexity of subset interconnection designs. J Glob Optim 6, 193–205 (1995). https://doi.org/10.1007/BF01096768
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DOI: https://doi.org/10.1007/BF01096768