Kruskal

# Kruskal - Rediscovered by Sollin in 1960s 2 Prim’s...

This preview shows pages 1–6. Sign up to view the full content.

1 Spanning Tree Set of edges connecting all nodes in graph need N-1 edges for N nodes no cycles, can be thought of as a tree Can build tree during traversal

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Minimum Spanning Tree (MST) Spanning tree with minimum total edge weight
3 Minimum Spanning Tree (MST) Possible to have multiple MSTs Different spanning trees with same weight Example applications Minimize length of telephone lines for neighborhood Minimize distance of airplane routes serving cities

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 Algorithms for Finding MST Three well known algorithms 1. Borůvka’s algorithm [1926] For constructing efficient electricity network

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Rediscovered by Sollin in 1960s 2. Prim’s algorithm [1957] First discovered by Vojtěch Jarník in 1930 Similar to Djikstra’s algorithm 3. Kruskal’s algorithm [1956] By Prof. Clyde Kruskal’s uncle 5 MST – Kruskal’s Algorithm sort edges by weight (from least to most) tree = for each edge (X,Y) in order if it does not create a cycle add (X,Y) to tree stop when tree has N–1 edges Keeps track of lightest edge remaining whether adding edge to MST creates cycle Optimal solution computed with greedy algorithm 6 MST – Kruskal’s Algorithm Example...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

Kruskal - Rediscovered by Sollin in 1960s 2 Prim’s...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online