Minimum Spanning Tree: Difference between revisions
From Rice Wiki
No edit summary |
|||
| Line 15: | Line 15: | ||
of <math>T</math> vs. <math>V - T</math> | of <math>T</math> vs. <math>V - T</math> | ||
Given the MST of <math>V_{n - 1} </math>, the MST of <math>V</math> | Given the MST of <math>V_{n - 1} = v_1, v_2, \ldots, v_{n-1} </math>, | ||
should be that of <math>V_{n-1}</math> plus the edge that connects to | the MST of <math>V</math> should be that of <math>V_{n-1}</math> plus | ||
<math>v_n</math> that is the shortest. | the edge that connects to <math>v_n</math> that is the shortest. | ||
<math> | <math> | ||
Revision as of 01:24, 6 March 2024
A minimum spanning tree is
- a tree, meaning it has no cycle
- minimum, meaning it has minimum weight
- spanning, meaning it connects all nodes
MST Problem
The MST problem takes a connected graph and outputs an MST for that graph.
Approach: Greedy
The approach is to try to add the smallest edges as long as they do not create a cycle; add an edge to the tree that is minimum across the cut of vs.
Given the MST of , the MST of should be that of plus the edge that connects to that is the shortest.
