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# :ddrt (README)
A Dynamic, Distributed [R-Tree](https://en.wikipedia.org/wiki/R-tree) (__DDRT__) library written in Elixir. The 'dynamic' part of the title refers to the fact that this implementation is optimized for a high volume of update operations. Put another way, this is an R-tree best suited for use with spatial data _in constant movement_. The 'distributed' part refers to the fact that this library is designed to maintain a spatial index (rtree) across a cluster of distributed elixir nodes.
The library uses [@derekkraan](https://github.com/derekkraan)'s [MerkleMap](https://github.com/derekkraan/merkle_map) and [CRDT](https://github.com/derekkraan/delta_crdt_ex) implementations to ensure reliable, "eventually consistent" distributed behavior.
The complete documentation is [available on hexdocs](https://hexdocs.pm/ddrt). You can find the hex package [here](https://hex.pm/packages/ddrt).
# Getting Started
## Installation
The package can be installed
by adding `ddrt` to your list of dependencies in `mix.exs`:
```elixir
def deps do
[
{:ddrt, "~> 0.2.1"}
]
end
```
## Starting DDRT Processes
Start up a DDRT process with default values
```elixir
DDRT.start_link([
name: DDRT
width: 6,
verbose: false,
seed: 0
])
```
Or add it to your supervision tree:
```elixir
Supervisor.start_link([
{DDRT, [
name: DDRT,
width: 6,
verbose: false,
seed: 0
]}
], [name: MySupervisor])
```
Otherwise if you're just looking to use the standalone R-tree functionality on a single machine (not a cluster of machines), you would instead use the `DDRT.DynamicRtree` module:
```elixir
DDRT.DynamicRtree.start_link([name: DynamicRtree])
```
Note: all configuration parameters and public API methods are _exactly_ the same between the `DDRT` and `DDRT.DynamicRtree` modules.
## Configuration
Available configuration parameters are:
- **name**: The name of the DDRT process. Defaults to `DDRT`
- **width**: The max number of children a node may have. Defaults to `6`
- **verbose**: allows `Logger` to report console logs. (Also decreases performance). Defaults to `false`.
- **seed**: Sets the seed value for the pseudo-random number generator which generates the unique IDs for each node in the tree. This is a deterministic process; so the same seed value will guarantee the same pseudo-random unique IDs being generated for your tree in the same order each time. Defaults to `0`
## Replicating your R-Tree in a cluster
First it's important to understand that distributed networking capabilities come built-in with Erlang. To get Elixir processes communicating amongst themselves over a network in general, we first have to use that fundamental Erlang networking magic to make all of the running Erlang Virtual Machines "aware" of eachother's existence on the network. In Elixir, these concepts are expressed in the [Node](https://hexdocs.pm/elixir/Node.html) module. One can use `Node.connect/2`
to make two Erlang VM nodes aware of eachother, and then Elixir processes are able to send messages to eachother on those nodes.
Connecting up the Erlang VMs in your cluster is outside of the scope of this package. There are already other libraries in Elixir designed to do exactly this. Possibly the best example is [`bitwalker/libcluster`](https://github.com/bitwalker/libcluster).
A very simple `libcluster` configuration for quick and easy development might look like:
```elixir
## config.exs ##
use Mix.Config
config :libcluster,
topologies: [
example: [
strategy: Cluster.Strategy.Epmd,
config: [hosts: [:"a@localhost", :"b@localhost"]],
]
]
```
Then you would have to pass in those same node names to `iex` when you start your application, like:
```elixir
eduardo@ddrt $ iex --name a@localhost -S mix
iex(a@localhost)1>
eduardo@ddrt $ iex --name b@localhost -S mix
iex(b@localhost)1>
```
Finally, after starting DDRT on each node you would use `DDRT.set_members/2` to begin communication between DDRT processes like this:
```elixir
# on node A:
{:ok, _pid} = DDRT.start_link([name: DDRT])
DDRT.set_members(DDRT, [{DDRT, :b@localhost}])
# on node B:
{:ok, _pid} = DDRT.start_link([name: DDRT])
DDRT.set_members(DDRT, [{DDRT, :a@localhost}])
```
From here, everything done on either tree will be reflected in the other tree.
Note: it's important that you have the same configuration parameters for each `DDRT` process running on each connected node in your cluster.
# Usage
Starts a local DDRT named `:peter`
```elixir
iex> DDRT.start_link([name: :peter])
{:ok, #PID<0.214.0>}
```
Insert "Griffin" into the `:peter` DDRT
```elixir
iex> DDRT.insert({"Griffin", [{4,5}, {6,7}]}, :peter)
{:ok,
%{
43143342109176739 => {["Griffin"], nil, [{4, 5}, {6, 7}]},
:root => 43143342109176739,
:ticket => [19125803434255161 | 82545666616502197],
"Griffin" => {:leaf, 43143342109176739, [{4, 5}, {6, 7}]}
}}
```
Insert "Parker" on into the `:peter` DDRT
```elixir
iex> DDRT.insert({"Parker",[{10,11},{16,17}]},:peter)
{:ok,
%{
43143342109176739 => {["Parker", "Griffin"], nil, [{4, 11}, {6, 17}]},
:root => 43143342109176739,
:ticket => [19125803434255161 | 82545666616502197],
"Griffin" => {:leaf, 43143342109176739, [{4, 5}, {6, 7}]},
"Parker" => {:leaf, 43143342109176739, [{10, 11}, {16, 17}]}
}}
```
Query which leaves in the `:peter` R-tree overlap with box `[{0,7},{4,8}]`
```elixir
iex> DDRT.query([{0,7},{4,8}],:peter)
{:ok, ["Griffin"]}
```
Updates "Griffin" bounding box in the `:peter` R-tree
```elixir
iex> DDRT.update("Griffin", [{-6,-5},{11,12}], :peter)
{:ok,
%{
43143342109176739 => {["Parker", "Griffin"], nil, [{-6, 11}, {6, 17}]},
:root => 43143342109176739,
:ticket => [19125803434255161 | 82545666616502197],
"Griffin" => {:leaf, 43143342109176739, [{-6, -5}, {11, 12}]},
"Parker" => {:leaf, 43143342109176739, [{10, 11}, {16, 17}]}
}}
```
Repeat the last query again. (This time "Griffin" is no longer within the query bounding box.)
```elixir
iex> DDRT.query([{0,7},{4,8}], :peter)
{:ok, []}
```
Now lets delete both "Griffin" and "Parker" keys from the tree.
```elixir
iex> DDRT.delete(["Griffin","Parker"], :peter)
{:ok,
%{
43143342109176739 => {[], nil, [{0, 0}, {0, 0}]},
:root => 43143342109176739,
:ticket => [19125803434255161 | 82545666616502197]
}}
```
### Bounding-Box Format
`[{x_min,x_max}, {y_min,y_max}]`
```elixir
Example: & & & & & y_max & & & & &
A unit at pos x: 10, y: -12 , & &
with x_size: 1 and y_size: 2 & &
would be represented with & pos &
the following bounding box x_min (x,y) x_max
[{9.5,10.5},{-13,-11}] & &
& &
& &
& & & & & y_min & & & & &
```
### Standalone (non-distributed) R-tree mode
If you're only interested in using an R-tree on a single machine in Elixir, you should be using the `DDRT.DynamicRtree` module. This module is optimized to run on a single machine, and as such the r-tree is significantly faster without the distribution overhead.
The `DDRT.DynamicRtree` module shares the same API and initialization options as the main `DDRT` module.
## Benchmarks
```elixir
Operating System: macOS
CPU Information: Intel(R) Core(TM) i5-5257U CPU @ 2.70GHz
Number of Available Cores: 4
Available memory: 8 GB
Elixir 1.9.0
Erlang 22.0.7
```
### Delete
```elixir
Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
parallel: 1
inputs: delete all leaves of tree [1000]
Estimated total run time: 28 s
##### With input delete all leaves of tree [1000] #####
Name ips average deviation median 99th %
map bulk 175.20 5.71 ms ±9.18% 5.60 ms 9.47 ms
merklemap bulk 80.27 12.46 ms ±21.27% 11.74 ms 25.37 ms
map 1 by 1 4.68 213.68 ms ±3.12% 213.24 ms 227.16 ms
merklemap 1 by 1 1.55 643.75 ms ±14.80% 616.84 ms 878.20 ms
Comparison:
map bulk 175.20
merklemap bulk 80.27 - 2.18x slower +6.75 ms
map 1 by 1 4.68 - 37.44x slower +207.97 ms
merklemap 1 by 1 1.55 - 112.79x slower +638.04 ms
```
### Update
```elixir
Benchmark suite executing with the following configuration:
warmup: 2 s
time: 10 s
memory time: 0 ns
parallel: 1
inputs: all leaves of tree [1000], all leaves of tree [100000]
Estimated total run time: 48 s
##### With input all leaves of tree [1000] #####
Name ips average deviation median 99th %
map 133.88 7.47 ms ±22.82% 6.92 ms 14.83 ms
merklemap 65.74 15.21 ms ±21.93% 14.18 ms 26.42 ms
Comparison:
map 133.88
merklemap 65.74 - 2.04x slower +7.74 ms
##### With input all leaves of tree [100000] #####
Name ips average deviation median 99th %
map 0.68 1.46 s ±15.84% 1.47 s 1.82 s
merklemap 0.33 3.01 s ±8.23% 3.09 s 3.21 s
Comparison:
map 0.68
merklemap 0.33 - 2.06x slower +1.55 s
```
### Query
```elixir
Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
parallel: 1
inputs: 100x100 box query, 10x10 box query, 1x1 box query, world box query
Estimated total run time: 56 s
##### With input 100x100 box query #####
Name ips average deviation median 99th %
merklemap 299.97 3.33 ms ±28.87% 3.03 ms 6.92 ms
map 268.51 3.72 ms ±36.46% 3.35 ms 8.57 ms
Comparison:
merklemap 299.97
map 268.51 - 1.12x slower +0.39 ms
##### With input 10x10 box query #####
Name ips average deviation median 99th %
map 1.50 K 667.16 μs ±37.04% 594 μs 1557.56 μs
merklemap 1.01 K 992.92 μs ±48.86% 883 μs 2418.52 μs
Comparison:
map 1.50 K
merklemap 1.01 K - 1.49x slower +325.76 μs
##### With input 1x1 box query #####
Name ips average deviation median 99th %
map 2.01 K 498.54 μs ±39.28% 430 μs 1257 μs
merklemap 1.51 K 660.89 μs ±45.08% 603 μs 1551.25 μs
Comparison:
map 2.01 K
merklemap 1.51 K - 1.33x slower +162.34 μs
##### With input world box query #####
Name ips average deviation median 99th %
map 156.18 6.40 ms ±18.51% 5.99 ms 10.70 ms
merklemap 152.11 6.57 ms ±26.12% 5.92 ms 13.93 ms
Comparison:
map 156.18
merklemap 152.11 - 1.03x slower +0.171 ms
```
### Insert
```elixir
Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
parallel: 1
inputs: 1000 leaves
Estimated total run time: 28 s
##### With input 1000 leaves #####
Name ips average deviation median 99th %
map bulk 305.53 3.27 ms ±39.39% 2.79 ms 7.96 ms
merklemap bulk 190.61 5.25 ms ±62.06% 4.37 ms 17.65 ms
map 1 by 1 66.73 14.99 ms ±4.63% 14.78 ms 19.11 ms
merklemap 1 by 1 23.00 43.48 ms ±23.79% 39.24 ms 81.16 ms
Comparison:
map bulk 305.53
merklemap bulk 190.61 - 1.60x slower +1.97 ms
map 1 by 1 66.73 - 4.58x slower +11.71 ms
merklemap 1 by 1 23.00 - 13.28x slower +40.21 ms
```
