The Optrees package in R provides tools for solving optimal tree problems in weighted graphs, such as minimum cost spanning trees, minimum cost arborescences, shortest path trees, and maximum flow calculations. Examples demonstrate the use of various algorithms like Prim, Kruskal, and Dijkstra for obtaining minimum spanning trees and shortest path trees. Additionally, the package supports negative weight graphs and maximum flow calculations using the Ford-Fulkerson algorithm.

1. Prepared by Volkan OBAN
optrees package in R
Finds optimal trees in weighted graphs. In particular, this package provid
es solving tools for minimum costspanning tree problems,minimum cost
arborescenceproblems,shortestpath tree problems and minimum cut tr
ee problem.
Examples:
Minimum Spanning Tree
>nodes <- 1:4
> arcs <- matrix(c(1,2,2, 1,3,15, 1,4,3, 2,3,1, 2,4,9, 3,4,1),
+ ncol = 3, byrow = TRUE)
> # Minimum cost spanning tree with several algorithms
> getMinimumSpanningTree(nodes, arcs, algorithm = "Prim")
Minimum Cost Spanning Tree
Algorithm: Prim
Stages: 3 | Time: 0
------------------------------
ept1 ept2 weight
1 2 2
2 3 1
3 4 1
------------------------------
Total = 4
> getMinimumSpanningTree(nodes, arcs, algorithm = "Kruskal")
Minimum Cost Spanning Tree
Algorithm: Kruskal
Stages: 3 | Time: 0

2. ------------------------------
ept1 ept2 weight
2 3 1
3 4 1
1 2 2
------------------------------
Total = 4
> getMinimumSpanningTree(nodes, arcs, algorithm = "Boruvka")
Minimum Cost Spanning Tree
Algorithm: Boruvka
Stages: 1 | Time: 0
------------------------------
ept1 ept2 weight
1 2 2
2 3 1
3 4 1
------------------------------
Total = 4
Shortest Path Tree:
> nodes <- 1:5
> arcs <- matrix(c(1,2,2, 1,3,2, 1,4,3, 2,5,5, 3,2,4, 3,5,3, 4,3,1, 4,5,0),
+ ncol = 3, byrow = TRUE)
> # Shortest path tree
> getShortestPathTree(nodes, arcs, algorithm = "Dijkstra", directed=FALSE)
Shortest path tree
Algorithm: Dijkstra
Stages: 4 | Time: 0
------------------------------
ept1 ept2 weight
1 2 2
1 3 2
1 4 3
4 5 0
------------------------------
Total = 7
Distances from source:
------------------------------
source node distance
1 2 2
1 3 2
1 4 3
1 5 3
------------------------------
> getShortestPathTree(nodes, arcs, algorithm = "Bellman-Ford", directed=FAL
SE)
Shortest path tree

3. Algorithm: Bellman-Ford
Stages: 4 | Time: 0
------------------------------
ept1 ept2 weight
1 2 2
1 3 2
1 4 3
4 5 0
------------------------------
Total = 7
Distances from source:
------------------------------
source node distance
1 2 2
1 3 2
1 4 3
1 5 3
------------------------------
> # Graph with negative weights
> nodes <- 1:5
> arcs <- matrix(c(1,2,6, 1,3,7, 2,3,8, 2,4,5, 2,5,-4, 3,4,-3, 3,5,9, 4,2,-
2,
+ 5,1,2, 5,4,7), ncol = 3, byrow = TRUE)
> # Shortest path tree
> getShortestPathTree(nodes, arcs, algorithm = "Bellman-Ford", directed=TRU
E)
Shortest path tree
Algorithm: Bellman-Ford
Stages: 4 | Time: 0.09
------------------------------
head tail weight
1 3 7
2 5 -4
3 4 -3
4 2 -2
------------------------------
Total = -2
Distances from source:
------------------------------
source node distance
1 2 2
1 3 7
1 4 4
1 5 -2
------------------------------
Maximum flow:
> # Graph
> nodes <- 1:6
> arcs <- matrix(c(1,2,1, 1,3,7, 2,3,1, 2,4,3, 2,5,2, 3,5,4, 4,5,1, 4,6,6,
+ 5,6,2), byrow = TRUE, ncol = 3)
> # Maximum flow with Ford-Fulkerson algorithm

4. > maxFlowFordFulkerson(nodes, arcs, source.node = 2, sink.node = 6)
$s.cut
[1] 2 3 1 5
$t.cut
[1] 4 6
$max.flow
[1] 6