[5], which uses most of the structure theory of the Graph Minors project of Robertson and Seymour [6]). The second part of this article looks at these positive techniques systematically, and we hope that the reader will find useful tools there. This area is still rapidly developing, and ...
quantum annealing. Third, the solution is unembedded and is returned to the user. Notably, the process of finding an optimal graph-minor embedding is NP-hard. However, heuristic algorithms exist for finding graph minors51, and the D-Wave system implements its automatic embedding and unembedding ...
Interestingly, for a large family of plane graphs, the problemsAreaUniversalityandAreaUniversality≥0coincide: A compactness argument shows that for the area-universality of a triangulation (even more generally, for every plane graph with a triangular outer face) it makes in fact no difference whethe...
From this rate, we include in Fig. 3 a graph estimating the complexity of the precomputation based on this region of analyticity. Fig. 3 Conversion of a degree-n expansion in modified generalized Laguerre polynomials q_n^{(0.25)}(x;\gamma =0.1) with standard normally distributed pseudorandom...
(n3) algorithm for deciding membership in any minor-closed family of graphs, because such a family can be characterized by a finite collection of excluded minors [42]. Unfortunately, this approach is not explicit. More precisely, the graph minor theorem is not constructive; in general, we do...
4. The graph of two-dimensional Delone triangulations. group actions and there are only finitely many, as shown by Voronoi [64, Section 98] (see also Chapter 13.3 of [30]). Altogether we get: Theorem 5.3 (Main Theorem of Voronoi's Reduction Theory). The secondary cone of a Delone ...
This means identifying the isomorphism type of the incidence graph of the 20 vertices and the 27 tetrahedra. The software nauty [18] is a standard tool for this task. It computes a canonical hash value, which is a 64-Bit integer that encodes the isomorphism type. This hash value is also...
1Introduction We present a variational model for the matching of surfaces implicitly represented as level sets. The approach is inspired by the mathematical theory of nonlinear elasticity of thin shells. The model consists in an energy functional, which is to be minimized among deformations of a c...
Gurtin M (1972) The Linear Theory of Elasticity. In: Truesdell C (ed) Encyclopedia of Physics VIa, Vol II, Springer-Verlag, Berlin, pp 1–295 (reprinted as Mechanics of Solids, vol II. Springer, Berlin) Guyan RJ (1965) Reduction of stiffness and mass matrices. AIAA J 3:380 Article ...
Once roadmaps are computed with singly exponential complexity, questions about connectivity are reduced to the same questions in a finite graph, and can be answered with complexity no greater than polynomial in the size of the roadmap itself. All known algorithms for computing roadmaps follow a ...