Journal of Heuristics

, Volume 21, Issue 4, pp 479–499 | Cite as

A matheuristic for the minimum weight rooted arborescence problem

  • Christian BlumEmail author
  • Borja Calvo


The combinatorial optimization problem tackled in this work is from the family of minimum weight rooted arborescence problems. The problem is NP-hard and has applications, for example, in computer vision and in multistage production planning. We describe an algorithm which makes use of a mathematical programming solver in order to find near-optimal solutions to the problem both in acyclic directed graphs and in directed graphs possibly containing directed circuits. It is shown that the proposed technique compares favorably to competiting approaches published in the related literature. Moreover, the experimental evaluation demonstrates that, although mathematical programming solvers are very powerful for this problem, with growing graph size and density they become unpractical due to excessive memory requirements.


Combinatorial optimization Matheuristics Minimum weight rooted arborescence problem 



This work was supported by Grants TIN2012-37930-02 and TIN2013-41272P of the Spanish Government and by Grant IT-609-13 of the Basque Government. In addition, support is acknowledged from IKERBASQUE (Basque Foundation for Science). Our experiments have been executed in the High Performance Computing environment managed by RDlab ( and we would like to thank them for their support.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.University of the Basque Country UPV/EHUSan SebastianSpain
  2. 2.Ikerbasque, Basque Foundation for ScienceBilbaoSpain

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