Abstract
Many constraints on graphs, e.g. the existence of a simple path between two vertices, or the connectedness of the subgraph induced by some selection of vertices, can be straightforwardly represented by means of a suitable acyclicity constraint. One method for encoding such a constraint in terms of simple, local constraints uses a 3-valued variable for each edge, and an \((N+1)\)-valued variable for each vertex, where N is the number of vertices in the entire graph. For graphs with many vertices, this can be somewhat inefficient in terms of space usage.
In this paper, we show how to refine this encoding into one that uses only a single bit of information, i.e. a 2-valued variable, per vertex, assuming the graph in question is planar. We furthermore show how this same constraint can be used to encode connectedness constraints, and a variety of other graph-related constraints.
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References
Rintanen, J., Janhunen, T., Gebser, M.: SAT modulo graphs: acyclicity. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS, vol. 8761, pp. 137–151. Springer, Heidelberg (2014)
Grünbaum, B., Shephard, G.C.: Rotation and winding numbers for planar polygons and curves. Trans. Am. Math. Soc. 322(1), 169–187 (1990)
Otten, R., Van Wijk, J.: Graph representations in interactive layout design. In: Proceedings of the IEEE International Symposium on Circuits and Systems, pp. 914–918 (1978)
Rosenstiehl, P., Tarjan, R.E.: Rectilinear planar layouts and bipolar orientations of planar graphs. Discrete Comput. Geom. 1(1), 343–353 (1986)
Tamura, N.: Solving puzzles with Sugar constraint solver. Slides, August 2008. http://bach.istc.kobe-u.ac.jp/sugar/puzzles/sugar-puzzles.pdf
Tamura, N., Taga, A., Kitagawa, S., Banbara, M.: Compiling finite linear CSP into SAT. Constraints 14(2), 254–272 (2009)
Whitney, H.: On regular closed curves in the plane. Compositio Mathematica 4, 276–284 (1937)
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This work is funded by the ERC Advanced Grant ProofCert.
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Brock-Nannestad, T. (2016). Space-Efficient Planar Acyclicity Constraints. In: Kiselyov, O., King, A. (eds) Functional and Logic Programming. FLOPS 2016. Lecture Notes in Computer Science(), vol 9613. Springer, Cham. https://doi.org/10.1007/978-3-319-29604-3_7
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DOI: https://doi.org/10.1007/978-3-319-29604-3_7
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