For Cypher to think a cartesian project and expand into is the most efficient plan must mean that it thinks the cardinality of the combined labels is very low. It could think this if the individual label cardinality is relatively low, and it has no idea of correlation between cardinalities. For example, if the cardinality of (n:A) is 10% of all nodes, and the cardinality of (n:B) is also 10%, we would model the cardinality of (n:A:B) as 1% (ie. 0.1*0.1=0.01). But if many :A are also :B, then this calculation is very inaccurate, and for full correlation between :A and :B we should use the minimum of the two, which in my example would be 10% instead of 1%.

Could you let us know what the relative cardinalities are? Is there a correlation between nodes of the two types?

I have two more suggestions for making your query faster. One is to try your trick with only one label, and then before the RETURN, add an extra WITH vi, ph, 1 AS ignore WHERE vi:VI_PH_xxxx RETURN DISTINCT(ph).

The other suggestion is based on the fact that you seem to only want to know the number of unique ph for which there exists any relationship of that pattern, but are not interested in the count of relationships themselves. For this there is a specific syntax:

```
MATCH (ph:PH_VI_xxxx)
WHERE (vi:VI_PS_xxxx:VI_PH_xxxx)-[:VI_PH]->(ph)
RETURN count(DISTINCT ph) AS PH_Id
```