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

Ante Ćustić () and Abraham P. Punnen ()
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Ante Ćustić: Simon Fraser University Surrey
Abraham P. Punnen: Simon Fraser University Surrey

Journal of Combinatorial Optimization, 2018, vol. 35, issue 2, No 9, 436-453

Abstract: Abstract We investigate special cases of the quadratic minimum spanning tree problem (QMSTP) on a graph $$G=(V,E)$$ 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 $$O(|E|^2)$$ 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.

Keywords: Minimum spanning tree; Quadratic 0–1 problems; Quadratic minimum spanning tree; Polynomially solvable cases; Linearization (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-017-0184-3

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