allShortestPaths {e1071} R Documentation

## Find Shortest Paths Between All Nodes in a Directed Graph

### Description

`allShortestPaths` finds all shortest paths in a directed (or undirected) graph using Floyd's algorithm. `extractPath` can be used to actually extract the path between a given pair of nodes.

### Usage

```allShortestPaths(x)
extractPath(obj, start, end)
```

### Arguments

 `x` matrix or distance object `obj` return value of `allShortestPaths` `start` integer, starting point of path `end` integer, end point of path

### Details

If `x` is a matrix, then `x[i,j]` has to be the length of the direct path from point `i` to point `j`. If no direct connection from point `i` to point `j` exist, then `x[i,j]` should be either `NA` or `Inf`. Note that the graph can be directed, hence `x[i,j]` need not be the same as `x[j,i]`. The main diagonal of `x` is ignored. Alternatively, `x` can be a distance object as returned by `dist` (corresponding to an undirected graph).

### Value

`allShortestPaths` returns a list with components

 `length` A matrix with the total lengths of the shortest path between each pair of points. `middlePoints` A matrix giving a point in the middle of each shortest path (or 0 if the direct connection is the shortest path), this is mainly used as input for `extractPath`.

`extractPath` returns a vector of node numbers giving with the shortest path between two points.

Friedrich Leisch

### References

Kumar, V., Grama, A., Gupta, A. and Karypis, G. Introduction to Parallel Programming - Design and Analysis of Algorithms, Benjamin Cummings Publishing, 1994, ISBN 0-8053-3170-0

### Examples

```## build a graph with 5 nodes
x <- matrix(NA, 5, 5)
diag(x) <- 0
x[1,2] <- 30; x[1,3] <- 10
x[2,4] <- 70; x[2,5] <- 40
x[3,4] <- 50; x[3,5] <- 20
x[4,5] <- 60
x[5,4] <- 10
print(x)

## compute all path lengths
z <- allShortestPaths(x)
print(z)

## the following should give 1 -> 3 -> 5 -> 4
extractPath(z, 1, 4)
```

[Package e1071 version 1.5-2 Index]