Cube versus Torus Models for Combinatorial Optimization Problems and the Euclidean Minimum Spanning Tree Constant
Name
OR-234-90.pdf
Size
1.12 MB
Format
Adobe PDF
Checksum (MD5)
7ba1c813fec2b20d6928961c2dd9fbda
Author(s)
Jaillet, Patrick
Date Issued
November 1990
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 234-90
Abstract
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-torus model is in fact valid for the traditional d-cube model. For the MST, we also extend our result and show that stronger equivalences hold. Finally we present some remarks on the possible use of the d-torus model for exploring rates of convergence for the TSP in the square.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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