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. (This paper is an updated version of a tutorial published in 4'OR in 2008.)
https://hal-ensta-paris.archives-ouvertes.fr//hal-00975034
Contributor : Aurélien Arnoux
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Submitted on : Monday, April 7, 2014 - 5:40:31 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:04 AM
Dominique de Werra, Marie-Christine Costa, Christophe Picouleau, Bernard Ries. On the use of graphs in discrete tomography. Annals of Operations Research, Springer Verlag, 2010, 175, pp.287-307. ⟨10.1007/s10479-009-0649-6⟩. ⟨hal-00975034⟩
