About the Complexity of Timetables and 3-Dimensional Discrete Tomography: A Short Proof of NP-Hardness

Authors:
Yan Gerard
Affiliations:
Univ. Clermont 1, LAIC, Aubière, France 63172
Venue:
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Year:
2009

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Abstract

We consider the problem of 3-dimensional Discrete Tomography according to three linearly independent directions. Consistency of this problem has been proved to be NP-compete by M. Irving and R.W. Jerrum in 1993 [9] but there exists since 1976 a very close result of NP-hardness in the framework of Timetables which is due to S. Even, A. Itai, and A. Shamir [2]. The purpose of this paper is to provide a new result of NP-hardness for a very restricted class of 3D Discrete Tomography which is common with Timetables. Hence NP-hardness of 3D Discrete Tomography and of Timetables both follow from this new stronger result that we obtain with a short proof based on a generic principle.