MINIMAL KNOTS IN THE CUBIC LATTICE

How many edges are necessary and sufficient to construct a knot of type K in the cubic lattice? Define the minimal edge number of a knot to be this number of edges. To what extend does the minimal edge number measure the complexity of a knot? What is the behaviour of the minimal edge number under the connected sum of knots, and what is its limiting behaviour? We consider these questions and show that the minimal edge number may be computed using simulated annealing.