55 lines
1.8 KiB
Markdown
55 lines
1.8 KiB
Markdown
|
We tried generating a few sample graphs from the description given at
|
||
|
|
the in-person meetings. Then, we tried writing queries that would solve
|
||
|
|
the problem of updating nodes when a leaf value changes, assuming all the
|
||
|
|
internal nodes compute only the sum function.
|
||
|
|
|
||
|
|
We started by creating an index on `id` property to improve initial lookup
|
||
|
|
performance:
|
||
|
|
|
||
|
|
CREATE INDEX ON :Leaf(id)
|
||
|
|
|
||
|
|
Afther that, we set values of all leafs to 1:
|
||
|
|
|
||
|
|
MATCH (u:Leaf) SET u.value = 1
|
||
|
|
|
||
|
|
We then initialized the values of all other nodes in the graph:
|
||
|
|
|
||
|
|
MATCH (u) WHERE NOT u:Leaf SET u.value = 0
|
||
|
|
|
||
|
|
MATCH (u) WITH u
|
||
|
|
ORDER BY u.topological_index DESC
|
||
|
|
MATCH (u)-->(v) SET u.value = u.value + v.value
|
||
|
|
|
||
|
|
Leaf value change and update of affected values in the graph can
|
||
|
|
be done using three queries. To change the value of a leaf:
|
||
|
|
|
||
|
|
MATCH (u:Leaf {id: "18"}) SET u.value = 10
|
||
|
|
|
||
|
|
Then we had to reset all the affected nodes to the neutral element:
|
||
|
|
|
||
|
|
MATCH (u:Leaf {id: "18"})<-[* bfs]-(v)
|
||
|
|
WHERE NOT v:Leaf SET v.value = 0
|
||
|
|
|
||
|
|
Finally, we recalculated their values in topological order:
|
||
|
|
|
||
|
|
MATCH (u:Leaf {id: "18"})<-[* bfs]-(v)
|
||
|
|
WITH v ORDER BY v.topological_index DESC
|
||
|
|
MATCH (v)-->(w) SET v.value = v.value + w.value
|
||
|
|
|
||
|
|
There are a few assumptions necessary for the approach above to work.
|
||
|
|
|
||
|
|
* We are able to maintain topological order of vertices during graph
|
||
|
|
structure changes.
|
||
|
|
|
||
|
|
* It is possible to accumulate the value of the function. Formally:
|
||
|
|
$$f(x_1, x_2, ..., x_n) = g(...(g(g(x_1, x_2), x_3), ...), x_n)$$
|
||
|
|
|
||
|
|
* There is a neutral element for the operation. However, this
|
||
|
|
assumption can be dropped by introducing an artificial neutral element.
|
||
|
|
|
||
|
|
Above assumptions could be changed, relaxed or dropped, depending on the
|
||
|
|
specifics of the use case.
|
||
|
|
|
||
|
|
Number of operations required is proportional to the sum of degrees of affected
|
||
|
|
nodes.
|