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A characterization of linearizable instances of the quadratic minimum spanning tree problem

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Abstract

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.

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Acknowledgements

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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  1. Department of Mathematics, Simon Fraser University Surrey, 250-13450 102nd AV, Surrey, British Columbia, V3T 0A3, Canada

    Ante Ćustić & Abraham P. Punnen

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  1. Ante Ćustić
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  2. Abraham P. Punnen
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Correspondence to Ante Ćustić.

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Ćustić, A., Punnen, A.P. A characterization of linearizable instances of the quadratic minimum spanning tree problem. J Comb Optim 35, 436–453 (2018). https://doi.org/10.1007/s10878-017-0184-3

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