Abstract
This paper investigates the Euclidean length of a random walk though n coplanar points. The length of which has multiple applications including spanning trees, Steiner trees, and certain forms of the travelling salesman problem. To estimate this distance, we partition an area A into m equivalent squares and then add the expected Euclidean distances travelled between each of the m squares with the expected Euclidean distances travelled within each of the m squares. The end result is a closed form model for the expected length of a random walk through n coplanar points. Some avenues of future research are also included.
Original language | English |
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Pages (from-to) | 241-250 |
Number of pages | 10 |
Journal | International Journal of Mathematics in Operational Research |
Volume | 7 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2015 |
Keywords
- Euclidean travelling salesman problem
- Expected distance
- Random walk