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On the use of graphs in discrete tomography

4OR volume 6, pages 101–123 (2008)Cite this article

Abstract

In this tutorial paper, we consider the basic image reconstruction problem which stems from discrete tomography. We derive a graph theoretical model and we explore some variations and extensions of this model. This allows us to establish connections with scheduling and timetabling applications. The complexity status of these problems is studied and we exhibit some polynomially solvable cases. We show how various classical techniques of operations research like matching, 2-SAT, network flows are applied to derive some of these results.

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Authors and Affiliations

  1. ROSE, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Dominique de Werra & Bernard Ries

  2. CEDRIC CNAM, Paris, France

    Marie-Christine Costa & Christophe Picouleau

Authors
  1. Dominique de Werra
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  2. Marie-Christine Costa
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  3. Christophe Picouleau
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  4. Bernard Ries
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Correspondence to Dominique de Werra.

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de Werra, D., Costa, MC., Picouleau, C. et al. On the use of graphs in discrete tomography. 4OR 6, 101–123 (2008). https://doi.org/10.1007/s10288-008-0077-5

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  • DOI: https://doi.org/10.1007/s10288-008-0077-5

Keywords

  • Discrete tomography
  • Complete bipartite graph
  • Edge coloring
  • Timetabling
  • Constrained coloring
  • Scheduling

MSC classification (2000)

  • 05C15
  • 05C85
  • 90-01
  • 52C99