OJDM  Vol.8 No.4 , October 2018
L-Convex Polyominoes: Discrete Tomographical Aspects
Abstract: This paper uses the geometrical properties of L-convex polyominoes in order to reconstruct these polyominoes. The main idea is to modify some clauses to the original construction of Chrobak and Dürr in order to control the L-convexity using 2SAT satisfaction problem.
Cite this paper: Tawbe, K. and Mansour, S. (2018) L-Convex Polyominoes: Discrete Tomographical Aspects. Open Journal of Discrete Mathematics, 8, 116-136. doi: 10.4236/ojdm.2018.84009.

[1]   Barcucci, E., Del Lungo, A., Nivat, M. and Pinzani, R. (1996) Reconstructing Convex Polyominoes from Horizontal and Vertical Projections. Theoretical Computer Science, 155, 321-347.

[2]   Brunetti, S. and Daurat, A. (2005) Random Generation of Q-Convex Sets. Theoretical Computer Science, 347, 393-414.

[3]   Castiglione, G., Restivo, A. and Vaglica, R. (2006) A Reconstruction Algorithm for L-Convex Polyominoes. Theoretical Computer Science, 356, 58-72.

[4]   Castiglione, G., Frosini, A., Munarini, E., Restivo, A. and Rinaldi, S. (2007) Combinatorial Aspects of L-Convex Polyominoes. European Journal of Combinatorics, 28, 1724-1741.

[5]   Castiglione, G. and Restivo, A. (2003) Reconstruction of L-Convex Polyominoes. Electronic Notes on Discrete Mathematics, 12, 290-301.

[6]   Chrobak, M. and Durr, C. (1999) Reconstructing hv-Convex Polyominoes from Orthogonal Projections. Information Processing Letters, 69, 283-289.

[7]   Castiglione, G., Frosini, A., Restivo, A. and Rinaldi, S. (2005) A Tomographical Characterization of L-Convex Polyominoes. Lecture Notes in Computer Sciense, Vol. 3429. Proceedings of 12th International Conference on Discrete Geometry Fir Computer Imagery, DGCI, Poitiers, 2005, 115-125.

[8]   Tawbe, K. and Vuillon, L. (2011) 2L-Convex Polyominoes: Geometrical Aspects. Contributions to Discrete Mathematics, 6.