# Cube versus Torus Models for Combinatorial Optimization Problems and the Euclidean Minimum Spanning Tree Constant

@inproceedings{Jaillet1990CubeVT, title={Cube versus Torus Models for Combinatorial Optimization Problems and the Euclidean Minimum Spanning Tree Constant}, author={Patrick Jaillet}, year={1990} }

- Published 1990

For a sample of points drawn uniformly from either the d-dimensional torus or the d-cube, d > 2, we define a class of random processes with the property of being asymptotically equivalent in expectation in the two models. Examples include the traveling salesman problem (TSP), the minimum spanning tree problem (MST), etc. Application of this result helps closing down one open question: We prove that the analytical expression recently obtained by Avram and Bertsimas for the MST constant in the d… CONTINUE READING

#### Citations

##### Publications citing this paper.

SHOWING 1-2 OF 2 CITATIONS

## On properties of geometric random problems in the plane

VIEW 15 EXCERPTS

CITES BACKGROUND & METHODS

HIGHLY INFLUENCED

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 10 REFERENCES

## Growth Rates of Euclidean Minimal Spanning Trees with Power Weighted Edges

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL

## The Minimum Spanning Tree Constant in Geometrical Probability and under the Independent Model; a Unified Approach

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL

## The shortest path through many points

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## On the Largest Edge in a Minimum Spanning Tree in the Square

VIEW 2 EXCERPTS

## Probabilistic Analysis of Partitioning Algorithms for the Traveling Salesman Problem in the Plane

VIEW 1 EXCERPT

#### Similar Papers

Loading similar papers…