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Graphs: Minimum Spanning Tree Algorithms Prim’s KruskalPowerPoint Presentation

Graphs: Minimum Spanning Tree Algorithms Prim’s Kruskal

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Graphs: Minimum Spanning Tree Algorithms Prim’s Kruskal

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Graphs: Minimum Spanning Tree Algorithms Prim’s Kruskal

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Decision Maths 1

- Graphs:
- Minimum Spanning Tree Algorithms
- Prim’s
- Kruskal

Robert Clay Prim (born 1921 in Sweetwater, Texas) is an American mathematician and computer scientist.

In 1941, Prim received his B.S. in Electrical Engineering from Princeton University. Later in 1949, he received his Ph.D. in Mathematics there also.

During the climax of World War II (1941–1944), Prim worked as an engineer for General Electric. From 1944 until 1949, he was hired by the United States Naval Ordnance Lab as an engineer and later a mathematician. At Bell Laboratories, he served as director of mathematics research from 1958 to 1961. There, Prim developed Prim's algorithm.

Prim's algorithm, was originally discovered in 1930 by mathematician Vojtech Jarnik and later independently by Prim in 1957. It was later rediscovered by Edsger Dijkstra in 1959.

VojtěchJarník (Czech pronunciation: December 22, 1897 – September 22, 1970) was a Czech mathematician.

His main area of work was in number theory and mathematical analysis; he proved a number of results on lattice point problems. He also developed the graph theory algorithm known as Prim's algorithm.

Joseph Bernard Kruskal, Jr. (born January 29, 1928) is an American mathematician, statistician, computer scientist and psychometrician. He was a student at the University of Chicago and at Princeton University, where he completed his Ph.D in 1954.

In computer science, his best known work is Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph. The algorithm first orders the edges by weight and then proceeds through the ordered list adding an edge to the partial MST provided that adding the new edge does not create a cycle. Minimal spanning trees have applications to the construction and pricing of communication networks.

Kruskal also applied his work in linguistics, in an experimental lexicostatistical study of Indo-European languages, together with the linguists Isidore Dyen and Paul Black.

Find the minimum spanning tree for this network.

D

12

A

4

11

3

B

10

E

12

C

7

8

5

8

F

Prim’s Minimum Spanning Tree (a greedy algorithm)

Starting from C

During his career at Bell Laboratories, Robert Prim along with co-worker Joseph Kruskal developed two different algorithms for finding a minimum spanning tree.

D

12

A

4

4

11

11

3

3

B

10

E

12

C

7

7

8

5

5

Minimum weight = 30

8

F

This algorithm first appeared in Proceedings of the American Mathematical Society in 1956, and was written by Joseph Kruskal.

Kruskal’s minimum spanning tree algorihtm

D

12

A

4

4

11

11

3

3

B

10

E

12

C

7

7

8

5

5

8

F

Minimum weight = 30