A characterization of linearizable instances of the quadratic minimum spanning tree problem
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We investigate special cases of the quadratic minimum spanning tree problem (QMSTP) on a graph \(G=(V,E)\) that can be solved as a linear minimum spanning tree problem. We give a characterization of such problems when G is a complete graph, which is the standard case in the QMSTP literature. We extend our characterization to a larger class of graphs that include complete bipartite graphs and cactuses, among others. Our characterization can be verified in \(O(|E|^2)\) time. In the case of complete graphs and when the cost matrix is given in factored form, we show that our characterization can be verified in O(|E|) time. Related open problems are also indicated.
KeywordsMinimum spanning tree Quadratic 0–1 problems Quadratic minimum spanning tree Polynomially solvable cases Linearization
This research work was supported by an NSERC discovery Grant and an NSERC discovery accelerator supplement awarded to Abraham P. Punnen.
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