Reduction from three-dimensional discrete tomography to multicommodity flow problem

  • Authors:

  • Y. Gerard

  • Affiliations:

  • LLAIC, IUT, Ensemble Universitaire des Cézeaux, Aubière, France

  • Venue:
  • Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
  • Year:
  • 2005

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Abstract

The reduction from two-dimensional-discrete tomography to max-flow problem is well-known [Gale, A theorem on flows in networks, Pacific J. Math. 7 (1957) 1073-1082]. This approach is based on the natural correspondence between two-dimensional lattices and bipartite graphs. We extend this result in dimension 3 by reducing three-dimensional discrete tomography to multicommodity flow problems. Two reductions are presented, one considering discrete tomography with multisets while the other one works with sets.