We study the computational complexity of decision problems on triangulated 3-manifolds. In this setting there has been encouraging initial progress in recent years, but many important questions remain wide open. The “simple” problem of 3-sphere recognition and the related problem of unknot recognition are both known to be in NP, by work of Schleimer [18] and earlier work of Hass, Lagarias and P...

The generalised Sudoku problem with N symbols is known to be NP-complete, and hence is equivalent to any other NP-complete problem, even for the standard restricted version where N is a perfect square. In particular, generalised Sudoku is equivalent to the, classical, Hamiltonian cycle problem. A constructive algorithm is given that reduces generalised Sudoku to the Hamiltonian cycle problem, w...

Geodesic vector fields and other distinguished on a Riemann manifold were used in the study of free motions such manifold, we applied geometric Hamilton–Jacobi theory for search geodesic from same closed fields. These properties appropriately extended to framework Newtonian generalised systems, particular systems defined by Lagrangians mechanical type velocity-dependent forces. Conserved quanti...

We analyse the generalised assignment problem under the assumption that all coefficients are drawn uniformly and independently from [0,1]. We show that such problems can be solved exactly with high probability, in a well-defined sense. The results are closely related to earlier work of Lueker, Goldberg and Marchetti-Spaccamela and ourselves.

The aim of this paper is to present theoretical basis for computing a representation of a compact Riemann surface as an algebraic plane curve and to compute a numerical approximation for its period matrix. We will describe a program Cars ((3]) that can be used to deene Riemann surfaces for computations. Cars allows one also to perform the Fenchel{Nielsen twist and other deformations on Riemann ...