On the difficulty of embedding planar graphs with inaccuracies
In this paper it will be shown that the following problem is NP-hard. We are given a labeled planar graph, each vertex of which is assigned to a disc in the plane. Decide whether it is possible to embed the graph in the plane with line segments as edges such that each vertex lies in its disc.
KeywordsNormal Form Planar Graph Conjunctive Normal Form Truth Assignment Boolean Formula
- 1.Eades, P., Wormald, N.: Fixed Edge Length Graph Drawing is NP-hard. Discrete Applied Mathematics. 28 (1990) 111–134Google Scholar
- 2.Cook, S.: The complexity of theorem-proving procedures. Proc. 3rd Ann. ACM Symp. on Theory of Computing (assoc. Comput. Mach., New York, 1971) 151–158Google Scholar
- 3.Lichtenstein, D.: Planar formulae and their uses. SIAM Journal of Computing 11 (1982) no. 2, 329–343Google Scholar
- 4.Tovey, C.: A simplified NP-complete satisfiability problem. Discrete-Applied-Mathematics 8 (1984), no. 1, 85–89Google Scholar