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Algorithmic and structural aspects of the P 3-Radon number

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Abstract

The generalization of classical results about convex sets in ℝn to abstract convexity spaces, defined by sets of paths in graphs, leads to many challenging structural and algorithmic problems. Here we study the Radon number for the P 3-convexity on graphs. P 3-convexity has been proposed in connection with rumour and disease spreading processes in networks and the Radon number allows generalizations of Radon’s classical convexity result. We establish hardness results and describe efficient algorithms for trees.

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Acknowledgements

This work has been done in the context of the CAPES-DAAD PROBRAL project “Cycles, Convexity, and Searching in Graphs”. The first and fifth authors have been supported by CNPq and FAPERJ. The third author has been supported by FAPERJ. The sixth author has been supported by CAPES.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Mitre C. Dourado, Jayme L. Szwarcfiter & Alexandre Toman

  2. Institut für Optimierung und Operations Research, Universität Ulm, Ulm, Germany

    Dieter Rautenbach & Philipp M. Schäfer

  3. PESC, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Vinícius Fernandes dos Santos & Jayme L. Szwarcfiter

  4. NCE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Jayme L. Szwarcfiter

Authors
  1. Mitre C. Dourado
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  2. Dieter Rautenbach
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  3. Vinícius Fernandes dos Santos
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  4. Philipp M. Schäfer
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  5. Jayme L. Szwarcfiter
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  6. Alexandre Toman
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Correspondence to Dieter Rautenbach.

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Dourado, M.C., Rautenbach, D., dos Santos, V.F. et al. Algorithmic and structural aspects of the P 3-Radon number. Ann Oper Res 206, 75–91 (2013). https://doi.org/10.1007/s10479-013-1320-9

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  • DOI: https://doi.org/10.1007/s10479-013-1320-9

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