Download presentation

Presentation is loading. Please wait.

Published byBryan Johnston Modified over 5 years ago

1
Minimum spanning tree Prof Amir Geva Eitan Netzer

2
Definition A sub group of edges from weighted graph G Spanning – reach all vertex Minimal – the sum of its edges is the lowest of all spanning trees Uses – connect a network with while spending minimum money Graph need to be connective

4
Prim algorithm (1957) Greedy algorithm Start with an empty list of vertex. Choose starting vertex from G. Randomly or a given choice. Add edge with minimal weight that not used yet to an un explored vertex. Continue until list of vertex contain all vertex in G. Minimum edge weight data structureTime complexity (total) adjacency matrixadjacency matrix, searchingO(|V| 2 ) binary heapbinary heap and adjacency listadjacency listO((|V| + |E|) log |V|) = O(|E| log |V|) Fibonacci heapFibonacci heap and adjacency listadjacency listO(|E| + |V| log |V|)

5
Pseudo Code

16
Kruskal's algorithm (1956) Greedy algorithm Create a “forest” F a set of trees Create a set S containing all edges of G While S is not empty and F is not a spanning tree yet Remove minimum edge from S If edge connects to trees in F combine them Else discard edge

17
Pseudo Code

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google