`dodgr`

is an R package for efficient calculation of
many-to-many pairwise distances on dual-weighted directed graphs, for
aggregation of flows throughout networks, and for highly realistic
routing through street networks (time-based routing considering incline,
turn-angles, surface quality, everything).

Note that most `dodgr`

algorithms implement parallel
computation with the `RcppParallel`

library, and by default use the maximal number of available cores or
threads. If you do not wish `dodgr`

to use all available
threads, please reduce the number manually by first specifying a value
via

`::setThreadOptions (numThreads = 1L) # or desired number RcppParallel`

Four aspects. First, while other packages exist for calculating
distances on directed graphs, notably `igraph`

, even that
otherwise fabulous package does not (readily) permit analysis of
*dual-weighted* graphs. Dual-weighted graphs have two sets of
weights for each edge, so routing can be evaluated with one set of
weights, while distances can be calculated with the other. A canonical
example is a street network, where *weighted distances* are
assigned depending on mode of transport (for example, weighted distances
for pedestrians on multi-lane vehicular roads are longer than equivalent
distances along isolated walking paths), yet the desired output remains
direct, unweighted distances. Accurate calculation of distances on
street networks requires a dual-weighted representation. In
**R**, `dodgr`

is currently the only package
that offers this functionality (without excessive data wrangling).

Second, while `igraph`

and almost all other routing packages are primarily designed for
one-to-one routing, `dodgr`

is specifically designed for
many-to-many routing, and will generally outperform equivalent packages
in large routing tasks.

Third, `dodgr`

goes beyond the functionality of comparable
packages through including routines to aggregate flows throughout a
network, through specifying origins, destinations, and flow densities
between each pair of points. Alternatively, flows can be aggregated
according to a network dispersal model from a set of origin points and
associated densities, and a user-specified dispersal model.

Fourth and finally, `dodgr`

implements highly realistic
and fully-customisable profiles for routing through street networks with
various modes of transport, and using either distance- or time-based
routing. Routing can include such factors as waiting times at traffic
lights, delays for turning across oncoming traffic, access restrictions,
and the effects of elevation on both cyclists and pedestrians. See the
dedicated vignette on street
networks and time-based routing for more detail.

You can install latest stable version of `dodgr`

from CRAN
with:

`install.packages ("dodgr") # current CRAN version`

Alternatively, current development versions can be installed using any of the following options:

```
# install.packages("remotes")
::install_git ("https://git.sr.ht/~mpadge/dodgr")
remotes::install_git ("https://codeberg.org/UrbanAnalyst/dodgr")
remotes::install_bitbucket ("UrbanAnalyst/dodgr")
remotes::install_gitlab ("UrbanAnalyst/dodgr")
remotes::install_github ("UrbanAnalyst/dodgr") remotes
```

Then load with

```
library (dodgr)
packageVersion ("dodgr")
#> [1] '0.2.21'
```

While `dodgr`

works with any arbitrary networks, it also
includes numerous functions explicitly intended to be applied to
geodesic coordinates, which are identified whenever input data have
columns labelled “longitude” and “latitude”, or similar. Coordinates for
such data must be in the EPSG:4326 (WGS84) coordinate system.
`dodgr`

treats coordinates as numbers only, and it is up to
the user to ensure appropriate transformation to WGS84 coordinates prior
to submitting data to `dodgr`

functions.

`dodgr`

networksTo illustrate functionality, the package includes an example data set
containing the Open Street Map network for Hampi,
India (a primarily pedestrian village in the middle of a large World
Heritage zone). These data are in Simple Features
(`sf`

) format, as a collection of `LINESTRING`

objects. `dodgr`

represents networks as a simple rectangular
graph, with each row representing an edge segment between two points or
vertices. `sf`

-format objects can be converted to equivalent
`dodgr`

representations with the
`weight_streetnet()`

function:

```
class (hampi)
#> [1] "sf" "data.frame"
dim (hampi)
#> [1] 236 15
<- weight_streetnet (hampi, wt_profile = "foot")
graph class (graph)
#> [1] "data.frame" "dodgr_streetnet"
dim (graph)
#> [1] 6813 15
```

The `sf`

-format network contained 236
`LINESTRING`

objects, with the
`weight_streetnet()`

function decomposing these into 6,813
distinct edges, indicating that the `sf`

representation had
around 29 edges or segments in each `LINESTRING`

object. The
`dodgr`

network then looks like this:

`head (graph)`

geom_num | edge_id | from_id | from_lon | from_lat | to_id | to_lon | to_lat | d | d_weighted | highway | way_id | component | time | time_weighted |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 339318500 | 76.47491 | 15.34167 | 339318502 | 76.47612 | 15.34173 | 130.000241 | 130.000241 | path | 28565950 | 1 | 93.600174 | 93.600174 |

1 | 2 | 339318502 | 76.47612 | 15.34173 | 339318500 | 76.47491 | 15.34167 | 130.000241 | 130.000241 | path | 28565950 | 1 | 93.600174 | 93.600174 |

1 | 3 | 339318502 | 76.47612 | 15.34173 | 2398958028 | 76.47621 | 15.34174 | 8.890622 | 8.890622 | path | 28565950 | 1 | 6.401248 | 6.401248 |

1 | 4 | 2398958028 | 76.47621 | 15.34174 | 339318502 | 76.47612 | 15.34173 | 8.890622 | 8.890622 | path | 28565950 | 1 | 6.401248 | 6.401248 |

1 | 5 | 2398958028 | 76.47621 | 15.34174 | 1427116077 | 76.47628 | 15.34179 | 9.307736 | 9.307736 | path | 28565950 | 1 | 6.701570 | 6.701570 |

1 | 6 | 1427116077 | 76.47628 | 15.34179 | 2398958028 | 76.47621 | 15.34174 | 9.307736 | 9.307736 | path | 28565950 | 1 | 6.701570 | 6.701570 |

The `geom_num`

column maps directly onto the sequence of
`LINESTRING`

objects within the `sf`

-formatted
data. The `highway`

column is taken directly from Open Street
Map, and denotes the kind of “highway” represented by each edge. The
`component`

column is an integer value describing which of
the connected components of the network each edge belongs to (with
`1`

always being the largest component; `2`

the
second largest; and so on).

Note that the `d_weighted`

values are often greater than
the geometric distances, `d`

. In the example shown,
`service`

highways are not ideal for pedestrians, and so
weighted distances are slightly greater than actual distances. Compare
this with:

`head (graph [graph$highway == "path", ])`

geom_num | edge_id | from_id | from_lon | from_lat | to_id | to_lon | to_lat | d | d_weighted | highway | way_id | component | time | time_weighted |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 339318500 | 76.47491 | 15.34167 | 339318502 | 76.47612 | 15.34173 | 130.000241 | 130.000241 | path | 28565950 | 1 | 93.600174 | 93.600174 |

1 | 2 | 339318502 | 76.47612 | 15.34173 | 339318500 | 76.47491 | 15.34167 | 130.000241 | 130.000241 | path | 28565950 | 1 | 93.600174 | 93.600174 |

1 | 3 | 339318502 | 76.47612 | 15.34173 | 2398958028 | 76.47621 | 15.34174 | 8.890622 | 8.890622 | path | 28565950 | 1 | 6.401248 | 6.401248 |

1 | 4 | 2398958028 | 76.47621 | 15.34174 | 339318502 | 76.47612 | 15.34173 | 8.890622 | 8.890622 | path | 28565950 | 1 | 6.401248 | 6.401248 |

1 | 5 | 2398958028 | 76.47621 | 15.34174 | 1427116077 | 76.47628 | 15.34179 | 9.307736 | 9.307736 | path | 28565950 | 1 | 6.701570 | 6.701570 |

1 | 6 | 1427116077 | 76.47628 | 15.34179 | 2398958028 | 76.47621 | 15.34174 | 9.307736 | 9.307736 | path | 28565950 | 1 | 6.701570 | 6.701570 |

A `"path"`

offers ideal walking conditions, and so
weighted distances are equal to actual distances.

The many-to-many nature of `dodgr`

means that the function
to calculate distances, `dodgr_distances()`

or, for street networks, times, `dodgr_times()`

,
accepts two vectors or matrices of routing points as inputs (describing
origins and destinations), and returns a corresponding matrix of
pairwise distances. If an input graph has columns for both distances and
weighted distances, and/or times and weighted times, the weighted
versions are used to determine the effectively shortest or fastest
routes through a network, while actual distances or times are summed
along the routes to calculate final values. It is of course also
possible to calculate distances along fastest routes, times along
shortest routes, or any combination thereof, as detailed in the package
vignette on street
networks and time-based routing.

Routing points can, for example, be randomly selected from the
vertices of a graph. The vertices can in turn be extracted with the
`dodgr_vertices()`

function:

```
<- dodgr_vertices (graph)
v head (v)
```

id | x | y | component | n | |
---|---|---|---|---|---|

1 | 339318500 | 76.47491 | 15.34167 | 1 | 0 |

2 | 339318502 | 76.47612 | 15.34173 | 1 | 1 |

4 | 2398958028 | 76.47621 | 15.34174 | 1 | 2 |

6 | 1427116077 | 76.47628 | 15.34179 | 1 | 3 |

8 | 7799710916 | 76.47634 | 15.34184 | 1 | 4 |

10 | 339318503 | 76.47641 | 15.34190 | 1 | 5 |

For OSM data extracted with the `osmdata`

package (or,
equivalently, via the `dodgr::dodgr_streetnet()`

function),
each object (vertices, ways, and high-level relations between these
objects) is assigned a unique identifying number. These are retained
both in `osmdata`

and `dodgr`

, as the
`way_id`

column in the above `graph`

, and as the
`id`

column in the vertices. Random vertices may be generated
in this case through selecting `id`

values:

```
<- sample (v$id, size = 20)
from <- sample (v$id, size = 50)
to <- dodgr_dists (graph = graph, from = from, to = to)
d dim (d)
#> [1] 20 50
```

Alternatively, the points may be specified as matrices of geographic coordinates:

```
<- min (graph$from_lon) + runif (20) * diff (range (graph$from_lon))
from_x <- min (graph$from_lat) + runif (20) * diff (range (graph$from_lat))
from_y <- min (graph$from_lon) + runif (50) * diff (range (graph$from_lon))
to_x <- min (graph$from_lat) + runif (50) * diff (range (graph$from_lat))
to_y <- dodgr_dists (graph = graph, from = cbind (from_x, from_y), to = cbind (to_x, to_y)) d
```

In this case, the random points will be mapped on to the nearest points on the street network. This may, of course, map some points onto minor, disconnected components of the graph. This can be controlled either by reducing the graph to it’s largest connected component only:

```
<- graph [graph$component == 1, ]
graph nrow (graph)
```

or by explicitly using the `match_points_to_verts()`

function with the option `connected = TRUE`

:

```
<- match_points_to_verts (v, cbind (from_x, from_y), connected = TRUE)
from <- match_points_to_verts (v, cbind (to_x, to_y), connected = TRUE) to
```

This function returns an index into the result of
`dodgr_vertices`

, and so points to use for routing must then
be extracted as follows:

```
<- v$id [from] # or from <- v [from, c ("x", "y")]
from <- v$id [to]
to <- dodgr_dists (graph = graph, from = from, to = to) d
```

Flow aggregation refers to the procedure of routing along multiple
ways according to specified densities of flow between defined origin and
destination points, and aggregating flows along each edge of the
network. The procedure is functionally similar to the above procedure
for distances, with the addition of a matrix specifying pairwise flow
densities between the input set of origin (`from`

) and
destination (`to`

) points. The following example illustrates
use with a random “flow matrix”:

```
<- array (runif (length (from) * length (to)), dim = c (length (from), length (to)))
flows length (from)
#> [1] 20
length (to)
#> [1] 50
dim (flows)
#> [1] 20 50
<- dodgr_flows_aggregate (graph = graph, from = from, to = to, flows = flows) f
```

The result is simply the input `graph`

with an additional
column quantifying the aggregate flows along each edge:

`head (f)`

geom_num | edge_id | from_id | from_lon | from_lat | to_id | to_lon | to_lat | d | d_weighted | highway | way_id | component | time | time_weighted | flow |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 339318500 | 76.47491 | 15.34167 | 339318502 | 76.47612 | 15.34173 | 130.000241 | 130.000241 | path | 28565950 | 1 | 93.600174 | 93.600174 | 0.5815996 |

1 | 2 | 339318502 | 76.47612 | 15.34173 | 339318500 | 76.47491 | 15.34167 | 130.000241 | 130.000241 | path | 28565950 | 1 | 93.600174 | 93.600174 | 2.3630118 |

1 | 3 | 339318502 | 76.47612 | 15.34173 | 2398958028 | 76.47621 | 15.34174 | 8.890622 | 8.890622 | path | 28565950 | 1 | 6.401248 | 6.401248 | 0.5815996 |

1 | 4 | 2398958028 | 76.47621 | 15.34174 | 339318502 | 76.47612 | 15.34173 | 8.890622 | 8.890622 | path | 28565950 | 1 | 6.401248 | 6.401248 | 2.3630118 |

1 | 5 | 2398958028 | 76.47621 | 15.34174 | 1427116077 | 76.47628 | 15.34179 | 9.307736 | 9.307736 | path | 28565950 | 1 | 6.701570 | 6.701570 | 0.5815996 |

1 | 6 | 1427116077 | 76.47628 | 15.34179 | 2398958028 | 76.47621 | 15.34174 | 9.307736 | 9.307736 | path | 28565950 | 1 | 6.701570 | 6.701570 | 2.3630118 |

An additional flow aggregation function can be applied in cases where only densities at origin points are known, and movement throughout a graph is dispersive:

`<- dodgr_flows_disperse (graph = graph, from = from, dens = runif (length (from))) f `

For more detail, see the main package vignette, and the second vignette on street networks and time-based routing

All contributions to this project are gratefully acknowledged using
the `allcontributors`

package following the all-contributors specification.
Contributions of any kind are welcome!

mpadge |
karpfen |
Robinlovelace |
agila5 |
JimShady |
DavisVaughan |

layik |
olivroy |

virgesmith |
richardellison |
coatless |
znmeb |
yihui |
MartinLHazelton |