A Note on the Number of Leaves of a Euclidean Minimal Spanning Tree
We show that the number of vertices of degree k in the Euclidean minimal spanning tree through points drawn uniformly from either the d-dimensional torus or from the d-cube, d > 2, are asymptotically equivalent with probability one. Implications are discussed.
| Main Author: | |
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| Format: | Working Paper |
| Language: | en_US |
| Published: |
Massachusetts Institute of Technology, Operations Research Center
2004
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| Online Access: | http://hdl.handle.net/1721.1/5197 |
| _version_ | 1811084085911617536 |
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| author | Jaillet, Patrick |
| author_facet | Jaillet, Patrick |
| author_sort | Jaillet, Patrick |
| collection | MIT |
| description | We show that the number of vertices of degree k in the Euclidean minimal spanning tree through points drawn uniformly from either the d-dimensional torus or from the d-cube, d > 2, are asymptotically equivalent with probability one. Implications are discussed. |
| first_indexed | 2024-09-23T12:44:31Z |
| format | Working Paper |
| id | mit-1721.1/5197 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:44:31Z |
| publishDate | 2004 |
| publisher | Massachusetts Institute of Technology, Operations Research Center |
| record_format | dspace |
| spelling | mit-1721.1/51972019-04-12T13:40:47Z A Note on the Number of Leaves of a Euclidean Minimal Spanning Tree Jaillet, Patrick We show that the number of vertices of degree k in the Euclidean minimal spanning tree through points drawn uniformly from either the d-dimensional torus or from the d-cube, d > 2, are asymptotically equivalent with probability one. Implications are discussed. 2004-05-28T19:27:33Z 2004-05-28T19:27:33Z 1990-11 Working Paper http://hdl.handle.net/1721.1/5197 en_US Operations Research Center Working Paper;OR 235-90 380685 bytes application/pdf application/pdf Massachusetts Institute of Technology, Operations Research Center |
| spellingShingle | Jaillet, Patrick A Note on the Number of Leaves of a Euclidean Minimal Spanning Tree |
| title | A Note on the Number of Leaves of a Euclidean Minimal Spanning Tree |
| title_full | A Note on the Number of Leaves of a Euclidean Minimal Spanning Tree |
| title_fullStr | A Note on the Number of Leaves of a Euclidean Minimal Spanning Tree |
| title_full_unstemmed | A Note on the Number of Leaves of a Euclidean Minimal Spanning Tree |
| title_short | A Note on the Number of Leaves of a Euclidean Minimal Spanning Tree |
| title_sort | note on the number of leaves of a euclidean minimal spanning tree |
| url | http://hdl.handle.net/1721.1/5197 |
| work_keys_str_mv | AT jailletpatrick anoteonthenumberofleavesofaeuclideanminimalspanningtree AT jailletpatrick noteonthenumberofleavesofaeuclideanminimalspanningtree |