Démonstration Digital Twin Building Wire Management

Graph Data Science for
Digital Twin -
Wire Management
Graph Pattern Matching + GDS algorithms: computing at scale on your graph

Pierre Halftermeyer
Sr. Solutions Engineer
PhD in Graph Theory
3½ years at
pierre[AT]neo4j.com
Neo4j Inc. All rights reserved 2023
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Use case:
Optimal constrained
wire management
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Roadmap
Modeling and
Ingestion 1
3
2
4
Setting the problem
instance (sources and
targets)
Building full set of
possible connections
(constraint-compliant)
Apply GDS
algorithm

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Roadmap
Modeling and
Ingestion 1
3
2
4
Setting the problem
targets)
Apply GDS
algorithm

Ingest Minecraft-like
data
Unit voxels 3D grid modeling
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....................▢▢▢▢▢▢▢ +▢▢▢▢▢▢▢ ......................
....................+⍐+++++++++++⍐+......................
....................▢▢▢▢▢▢▢ +▢▢▢▢▢▢▢ ......................
....................+⍐+++++++++++⍐+......................
....................▢▢▢▢▢▢▢ +▢▢▢▢▢▢▢ ......................
.........................................................
# Floor 4
.........................................................
....................▢▢▢▢▢▢▢ +▢▢▢▢▢▢▢ ......................
....................+⍐+++++++++++⍐+......................
....................▢▢▢▢▢▢▢ +▢▢▢▢▢▢▢ ......................
....................▢▢▢▢▢▢▢ +▢▢▢▢▢▢▢ ......................
....................+⍐+++++++++++⍐+......................
....................▢▢▢▢▢▢▢ +▢▢▢▢▢▢▢ ......................
....................+⍐+++++++++++⍐+......................
....................▢▢▢▢▢▢▢ +▢▢▢▢▢▢▢ ......................
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▢ means :Voxel / Room by default
+ means :Lobby
⍐ means :Elevator:Bottom

Ingestion of (x, y, z) Voxels
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// parse csv
LOAD CSV FROM "file:///building.txt" AS line
WITH collect(line[0]) as lines
WITH [l IN lines | CASE WHEN l STARTS WITH "#" THEN "#" ELSE l
END] AS lines
CALL apoc.coll.split(lines, "#")
YIELD value
WITH value
WITH collect(value) AS building
WITH range(0, size(building)-1) AS ixs, building
WITH [ix IN ixs | {floor_num:ix+1, floor:building[ix]}] AS building
UNWIND building AS floor
WITH floor.floor_num AS z, floor.floor AS floor
UNWIND range(0, size(floor)-1) AS x
WITH z, x, floor[x] AS line
UNWIND range(0, size(line)-1) AS y
WITH z, x, y, substring(line,y,1) AS val
CREATE (:Voxel {x:x, y:y, z:z, val:val});
// Delete non relevant voxels
MATCH (n {val:'.'})
DELETE n;
// label Lobbys and Elevators
MATCH (s:Voxel WHERE s.val IN ["+", "⍐"])
SET s:Lobby;
MATCH (s:Voxel WHERE s.val IN ["⍐"])
SET s:Elevator:Bottom;

Connect adjacent
Voxels in 3D
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MATCH (s:Voxel)
WITH s.x AS x, s.y AS y, s.z AS z, s
ORDER BY z
WITH x, y, collect(s) AS line
CALL apoc.nodes.link(line, "HAS_ABOVE");
MATCH (a)-[r:HAS_ABOVE]->(b)
WHERE b.z - a.z <> 1
DELETE r;
MATCH (s:Voxel)
ORDER BY y
WITH x, z, collect(s) AS line
CALL apoc.nodes.link(line, "HAS_EAST");
MATCH (a)-[r:HAS_EAST]->(b)
WHERE b.y - a.y <> 1
DELETE r;
MATCH (s:Voxel)
ORDER BY x
WITH y, z, collect(s) AS line
CALL apoc.nodes.link(line, "HAS_NORTH");
MATCH (a)-[r:HAS_NORTH]->(b)
WHERE b.x - a.x <> 1

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Roadmap
Modeling and
Ingestion 1
3
2
4
Setting the problem
targets)
Building the full set of
possible wires
Apply GDS
algorithm

Rules
Let’s PoC with mock data
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If a wire has to join two Voxels from distinct
ﬂoors, pass the wire via the elevator.
No vertical drilling.
Our customer.
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Vertical connections use the Elevator
MATCH (a:!(Elevator&Bottom))-[r:HAS_ABOVE]->(b)
DELETE r;
MATCH (a:Elevator&Bottom)-[r:HAS_ABOVE]->(b)
SET b:Elevator:Top;
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Cables crossing room are possible but not
more than 3 rooms in a row. If more, you have
to pass via the lobby. Cable shouldn’t be
longer than 10 units of distance. This is
possible:
Voxel-Voxel-Voxel-Lobby-Lobby-Lobby-Voxel-Voxel
Our customer.
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1
0
u
n
i
t
s
m
a
x

Possible cable laying via Lobby.
MATCH (s:Voxel&!Lobby)
CALL {
WITH s
MATCH p=(s)(
()-[r1:HAS_NORTH|HAS_EAST]-(:Voxel&!Lobby)
){0,2}(:Voxel&!Lobby)-[:HAS_NORTH|HAS_EAST]-(:Lobby)(
()-[r2:HAS_EAST|HAS_NORTH|HAS_ABOVE]-(:Lobby)
){0,5}(:Lobby)-[:HAS_NORTH|HAS_EAST]-(:Voxel&!Lobby)(
){0,2}(t WHERE t<>s)
WITH s, t, size(r1+r2+r3)+2 AS wire_length,
[n IN nodes(p)|elementId(n)] AS intermediary_voxels
WHERE wire_length <= 10
CREATE (s)-[:LAYABLE_WIRE {cost:1+log(wire_length), intermediary_voxels:intermediary_voxels}]->(t)
} IN TRANSACTIONS OF 10 rows;
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Possible cable laying not via Lobby.
MATCH (s:Voxel)
CALL {
WITH s
MATCH p=(s)(
){1,2}(t:Voxel&!Lobby)
WITH s, t, size(r1) AS wire_length,
[n IN nodes(p)|elementId(n)] AS intermediary_voxels
WHERE wire_length <= 10
CREATE (s)-[:LAYABLE_WIRE {cost:log(1+wire_length), intermediary_voxels:intermediary_voxels}]->(t)
} IN TRANSACTIONS OF 10 rows;
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Roadmap
Modeling and
Ingestion 1
3
2
4
Setting the problem
targets)
Apply GDS
algorithm

IT Room and Target
Voxel
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MATCH (s:Voxel WHERE s.val = "▢")
WITH s, rand() AS ord
ORDER BY ord
LIMIT 3
SET s:ITRoom;
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Deﬁne IT Locals (randomly for demo)

MATCH (s:Voxel&!Lobby)
WHERE rand() < 0.50
SET s:Target;
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Deﬁne Target Locals (randomly for demo)

Each target room must be connected to at
least one IT room.
Our customer.
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Roadmap
Modeling and
Ingestion 1
3
2
4
Setting the problem
targets)
Run a GDS
algorithm

GDS Toolbox shortlist
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CREATE (sr:Voxel:Virtual:SteinerRoot);
MATCH (sr:SteinerRoot)
MATCH (li:ITRoom)
CREATE (sr)-[:LAYABLE_WIRE {cost:0.0}]->(li);

GDS in action
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Projecting the graph
CALL gds.graph.project(
'voxel_layable_wires_graph',
'Voxel',
{
LAYABLE_WIRE: {
properties: 'cost',
orientation: 'UNDIRECTED'
}
}
);
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Grow a Steiner Tree
MATCH (t:Target)
WITH collect(t) AS targets
MATCH (s:SteinerRoot)
WITH s, targets
CALL gds.beta.steinerTree.stream('voxel_layable_wires_graph',
{
sourceNode: id(s),
targetNodes: [t IN targets | id(t)],
relationshipWeightProperty:"cost"
})
YIELD nodeId, parentId, weight
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Build prettiﬁed Steiner Tree (Elbow Connector)
// remove Steiner root
MATCH (sr:SteinerRoot)
DETACH DELETE sr;
// create sections of cables to show elbow connections in Bloom
MATCH (a)-[r:STEINER_FOREST_WIRE]->(b)
WITH r, r.intermediary_voxels AS intermediary_voxels
WITH r, apoc.coll.zip(intermediary_voxels[..-1],intermediary_voxels[1..]) AS wire_lines
UNWIND wire_lines AS wire_line
WITH wire_line[0] AS line_from, wire_line[1] AS line_to, elementId(r) AS wire
MATCH (f WHERE elementId(f) = line_from), (t WHERE elementId(t) = line_to)
CREATE (f)-[:STEINER_FOREST_WIRE_CHUNK {connexion:wire}]->(t);
// Identify switches
MATCH (sw)
WHERE count{(sw)-[r:STEINER_FOREST_WIRE]->()} > 1
SET sw:Switch;
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Thank you!
name.name@neotechnology.com
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About yours truly
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Démonstration Digital Twin Building Wire Management

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