ArangoDB: Find all shortest paths - arangodb

Question

i want to get all shortest paths between 2 vertex.
Example: Give me all shortest path between node A and B should only return the 2 blue paths
this is what i have got so far:
LET source = (FOR x IN Entity FILTER x.objectID == "organization_1"
return x)[0]
LET destination = (FOR x IN Entity FILTER x.objectID == "organization_129"
return x)[0]
FOR node, edge, path IN 1..2 ANY source._id GRAPH "m"
FILTER LAST(path.vertices)._id == destination._id
LIMIT 100
RETURN path
Problems:
1. it is very slow (took 18 seconds on a graph with like 70 mio nodes)
2. it finds every path, but i want only all shortest path
UPDATE
i tried the 2-step query solution from the comments.
the problem is that the second query is also very slow
Query string:
FOR source IN Entity FILTER source.objectID == "organization_1"
LIMIT 1
FOR node, edge, path
IN 1..#depth ANY source._id
GRAPH "m"
OPTIONS {uniqueVertices: "path"}
FILTER node.objectID == "organization_129"
RETURN path
Execution plan:
Id NodeType Est. Comment
1 SingletonNode 1 * ROOT
11 IndexNode 1 - FOR source IN Entity /* hash index scan */
5 LimitNode 1 - LIMIT 0, 1
6 CalculationNode 1 - LET #6 = source.`_id` /* attribute expression */ /* collections used: source : Entity */
7 TraversalNode 346 - FOR node /* vertex */, path /* paths */ IN 1..2 /* min..maxPathDepth */ ANY #6 /* startnode */ GRAPH 'm'
8 CalculationNode 346 - LET #10 = (node.`objectID` == "organization_129") /* simple expression */
9 FilterNode 346 - FILTER #10
10 ReturnNode 346 - RETURN path
Indexes used:
By Type Collection Unique Sparse Selectivity Fields Ranges
11 hash Entity false false 100.00 % [ `objectID` ] (source.`objectID` == "organization_1")
7 edge ACTIVITYPARTY false false 100.00 % [ `_from`, `_to` ] base INBOUND
7 edge ACTIVITYPARTY false false 100.00 % [ `_from`, `_to` ] base OUTBOUND
7 edge ACTIVITY_LINK false false 100.00 % [ `_from`, `_to` ] base INBOUND
7 edge ACTIVITY_LINK false false 100.00 % [ `_from`, `_to` ] base OUTBOUND
7 edge ENTITY_LINK false false 70.38 % [ `_from`, `_to` ] base INBOUND
7 edge ENTITY_LINK false false 70.38 % [ `_from`, `_to` ] base OUTBOUND
7 edge RELATION false false 20.49 % [ `_from`, `_to` ] base INBOUND
7 edge RELATION false false 20.49 % [ `_from`, `_to` ] base OUTBOUND
7 edge SOFT_LINK false false 100.00 % [ `_from`, `_to` ] base INBOUND
7 edge SOFT_LINK false false 100.00 % [ `_from`, `_to` ] base OUTBOUND
Traversals on graphs:
Id Depth Vertex collections Edge collections Options Filter conditions
7 1..2 Activity, Entity, SOFT_LINK, Property ACTIVITYPARTY, ENTITY_LINK, SOFT_LINK, RELATION, ACTIVITY_LINK uniqueVertices: path, uniqueEdges: path
Optimization rules applied:
Id RuleName
1 move-calculations-up
2 move-filters-up
3 move-calculations-up-2
4 move-filters-up-2
5 use-indexes
6 remove-filter-covered-by-index
7 remove-unnecessary-calculations-2
8 optimize-traversals
9 move-calculations-down

Answer 1

First of all you need a hash index on field objectID in collection Entity to avoid the full collection scans, which heavily slows down your performance.
To get all shortest path I would first search for one shortest path with the AQL SHORTEST_PATH and return the number of visited vertices. There is also no need of subqueries (like in your query).
FOR source IN Entity FILTER source.objectID == "organization_1"
LIMIT 1
FOR destination IN Entity FILTER destination.objectID == "organization_129"
LIMIT 1
RETURN sum(
FOR v, e
IN ANY
SHORTEST_PATH source._id TO destination._id
GRAPH "m"
RETURN 1)-1
After that I would execute another query with the result from the first query as bind parameter #depth, which is used to limit the depth of the traversal.
FOR source IN Entity FILTER source.objectID == "organization_1"
LIMIT 1
FOR node, edge, path
IN 1..#depth ANY source._id
GRAPH "m"
OPTIONS {uniqueVertices: "path"}
FILTER node.objectID == "organization_129"
RETURN path
Note: To filter the last vertex in the path you don't have to use LAST(path.vertices), you can simply use node because it is already the last vertex (the same applies for edge).