Thesis supervisor: Lajos Hajdu
Location of studies (in Hungarian): Debreceni Egyetem Informatikai Kar Abbreviation of location of studies: DE IK
Description of the research topic:
The basic problem of discrete tomography is to reconstruct a binary (or, more generally an integer) matrix only knowing its line sums in certain directions. The field is relatively new, however, it already has a vast literature. The main problems are the questions of consistency (of the given line sums vector) and the uniqueness. In the latter problem, the so called switching components (configurations having zero line sums in the given directions) play an important role. For example, it is well-known that in case of two directions, the switching components are sufficient to describe completely the binary matrices having given line sums. In case of more directions the problem is much more difficult. (The questions arising are known to be NP hard.) Though the structure of switching components is well understood also in this case, however, this knowledge can be neatly applied only for integer matrices. In the frame of the doctoral subject, the applicability of this knowledge for binary matrices is planned to be investigated, both from algorithmic and theoretic points of view.
Bibliography
1. Discrete Tomography, International Journal of Imaging Systems and Technology 9, No. 2/3, Special Issue, (G. T. Herman and A. Kuba, eds.), 1998.
2. G. T. Herman and A. Kuba, Discrete Tomography: Foundations, Algorithms and Applications, Birkhäuser, Boston, 1999.
3. Linear Algebra and its Applications 339, Special issue on Discrete Tomography (A. Del Lungo, P. Gronchi and G. T. Herman, eds.), 2001.
4. Workshop on Discrete Tomography and Its Applications, Electronic Notes in Discrete Mathematics, Special Issue, (G. T. Herman and A. Kuba, eds.), 2005.
5. Advances in Discrete Tomography and Its Applications, (G.T. Herman, A. Kuba, eds.), Birkhäuser, 2007.
Recommended language skills (in Hungarian): angol Number of students who can be accepted: 1
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