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I extracted information from open street map that contains many polygons, some of them overlapping. I want to union all polygons that overlap with other polygons. This question has been asked before here: Dissolve only overlapping polygons in R but I am looking for an approach that uses the sf package.

Here is a reproducible example:

sq = function(pt, sz = 1) st_polygon(list(rbind(c(pt - sz), c(pt[1] + sz, pt[2] - sz), c(pt + sz), c(pt[1] - sz, pt[2] + sz), c(pt - sz))))
x = st_sf(box = 1:6, st_sfc(sq(c(4.2,4.2)), sq(c(0,0)), sq(c(1, -0.8)), sq(c(0.5, 1.7)), sq(c(3,3)), sq(c(-3, -3))))
plot(x)
st_overlaps(x)

What I am looking for is an appproach that unions the 2 rectangles that show overlap and the 3 rectangles that have overlap. Problem is that I do not know how to identify the 3 clusters of rectangles that I have in my example. With this information, I can run group_by %>% summarize() on the result and solve my problem.

enter image description here

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Here's my sample data:

> plot(bdf)

enter image description here

If you only care about whether polygons overlap and how they form clusters, then use st_intersects:

> st_intersects(bdf,bdf)
Sparse geometry binary predicate list of length 6, where the predicate was `intersects'
 1: 1
 2: 2, 3, 4
 3: 2, 3, 4
 4: 2, 3, 4
 5: 5, 6
 6: 5, 6

That gets you some of the way. The output above can be used to form an adjacency matrix of overlaps, which you can then feed into the igraph package to create a graph, and then you can get the disconnected subgraphs.

> library(igraph)
> g = st_intersects(bdf,bdf)
> plot(graph_from_adj_list(g))

enter image description here

Find the connected components with components:

> G = graph_from_adj_list(g)
> components(G)
$membership
[1] 1 2 2 2 3 3

$csize
[1] 1 3 2

$no
[1] 3

The $membership element of that list is telling you which cluster each of the six original features is a member of, in order.

Alternatively if you do want to construct the geometry of the clusters, use st_union:

> parts = st_cast(st_union(bdf),"POLYGON")

The output of st_union is a "MULTIPOLYGON" of three, so I split it into its "POLYGON" parts and then test intersection with the original features:

> st_intersects(bdf, parts)
Sparse geometry binary predicate list of length 6, where the predicate was `intersects'
 1: 1
 2: 3
 3: 3
 4: 3
 5: 2
 6: 2

which tells me that original feature 1 is in cluster 1, features 2 to 4 are in cluster 3, and features 5 and 6 form cluster 2.

Note the order is different from the igraph example - the ordering of the polygons from the st_union is not the same as the ordering of the connected components in the igraph example. From lower-left to upper right st_union has indexed the clusters 1,3,2 and igraph has indexed them 1,2,3. This ordering is arbitrary (but don't mix them up).

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These are great solutions. I used your second approach to solve my question above using the example I provide below. I determine the clusters, join them with the data and use group_by to union the polygons in the three clusters. Also added a paste statement to keep the names of the original polygons, something I need for my application:

sq = function(pt, sz = 1) st_polygon(list(rbind(c(pt - sz), c(pt[1] + sz, pt[2] - sz), c(pt + sz), c(pt[1] - sz, pt[2] + sz), c(pt - sz))))
x = st_sf(box = 1:6, st_sfc(sq(c(4.2,4.2)), sq(c(0,0)), sq(c(1, -0.8)), sq(c(0.5, 1.7)), sq(c(3,3)), sq(c(-3, -3))))
plot(x)

parts <- st_cast(st_union(x),"POLYGON")
plot(parts)

clust <- unlist(st_intersects(x, parts))

diss <- cbind(x, clust) %>%
  group_by(clust) %>%
  summarize(box = paste(box, collapse = ", "))

plot(diss[1])

enter image description here

Unfortunately, it seems that my actual data from Open Street Map is more messy than the example. When I use st_intersects to determine the links between the features and the clusters it appears that features can be related to two (or more) clusters. I do not understand how this is possible as then these two clusters should be regarded as one cluster.

The data can be found here. Perhaps you can have a look?

https://www.dropbox.com/s/4n259yhh5swqgf2/osm_data.rds?dl=0

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