Finds optimal trees in weighted graphs. In particular, this package provides solving tools for minimum cost spanning tree problems, minimum cost arborescence problems, shortest path tree problems and minimum cut tree problem. by Volkan OBAN

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