https://github.com/sleekpanther/reverse-delete-algorithm
Greedy Algorithm to find a minimum spanning tree in an undirected graph by deleting heaviest edges unless it would disconnect the graph
https://github.com/sleekpanther/reverse-delete-algorithm
algorithm algorithm-design algorithms edge graph greedy greedy-algorithms minimum-spanning-tree minimum-spanning-trees mst noah noah-patullo noahpatullo pattullo pattulo patullo patulo reverse-delete reverse-delete-algorithm tree
Last synced: 7 months ago
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Greedy Algorithm to find a minimum spanning tree in an undirected graph by deleting heaviest edges unless it would disconnect the graph
- Host: GitHub
- URL: https://github.com/sleekpanther/reverse-delete-algorithm
- Owner: SleekPanther
- Created: 2017-08-08T15:52:36.000Z (about 8 years ago)
- Default Branch: master
- Last Pushed: 2017-08-09T12:14:23.000Z (about 8 years ago)
- Last Synced: 2025-01-15T13:08:05.675Z (9 months ago)
- Topics: algorithm, algorithm-design, algorithms, edge, graph, greedy, greedy-algorithms, minimum-spanning-tree, minimum-spanning-trees, mst, noah, noah-patullo, noahpatullo, pattullo, pattulo, patullo, patulo, reverse-delete, reverse-delete-algorithm, tree
- Language: Java
- Homepage:
- Size: 123 KB
- Stars: 1
- Watchers: 2
- Forks: 3
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Reverse Delete Algorithm (Minimum Spanning Tree)
Greedy Algorithm to find a minimum spanning tree in an undirected graph by deleting heaviest edges unless it would disconnect the graph
## Problem Statement
**Minim Spanning Tree:** a subset of nodes that touches all vertices while keeping all nodes connected and uses the sum of the edge weights in a minimum
A Minimum spanning tree yields a graph with **M-1** edges because adding 1 more edge would by definition create a cycle
### Graph
### Minimum Spanning Tree
#### Weight = 18+14+9+7+6+5+2 = 61
## Reverse Delete Greedy Strategy
**Start with all edges in the tree T. Consider edges in descending order of weight. Delete edge from T unless doing so would disconnect T**
- Sort edges by weight
- Initialize MST with all edges
- Delete the highest weight edge
- If deleting the edge disconnects the graph, add it back
- Otherwise continue
## Usage
- Node names are consecutive integers starting from `0`
- Create a graph: `ArrayList graph = new ArrayList();`
- Graph undirected edge list, but **only add each edge once**
- In the graph there is an edge from `0` to `9` with weight=`9`
- This bidirectional edge can just be represented once: `graph.add(new Edge(0, 1, 9));`
- Count the vertices in the graph: `int vertexCount = 8;`
- Call the static method `ReverseDeleteMST.findMST(graph, vertexCount);`
# Code Notes
- Due to the implementation of Breadth First Search, the code creates an additional copy of the graph as an adjacency list
- This adjacency list graph is the one where edges are deleted, the original input graph as an edge list is left in tact
- The MST is technically built up from nothing and added to if deleting an edge in the adjacency list would disconnect the graph
## References
- [Kevin Wayne Slides](https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/04GreedyAlgorithmsII.pdf#page=14)
- [University of Illinois - Minimum Spanning Trees](https://courses.engr.illinois.edu/cs473/sp2011/Lectures/12_notes.pdf)
- [T. M. Murali Slides](http://courses.cs.vt.edu/cs5114/spring2009/lectures/lecture05-greedy-graph-algorithms.pdf#page=36)
- [Fan Chung Graham Slides](http://www.math.ucsd.edu/~fan/teach/202/14/04mst.pdf#page=11)
- [Reverse Delete Algorithm - GeeksForGeeks](http://www.geeksforgeeks.org/reverse-delete-algorithm-minimum-spanning-tree/) Algorithm strategy, code only briefly referenced
- [Remove items from ArrayList with certain value - Stack Overflow](https://stackoverflow.com/a/29107463/8132253) Lambda expression to delete specific value from `ArrayList`