How to find closest match between a given sentence and a sentence set

[SidWeng]

From the example DocumentSimilarityRankerApproach ranks among document. But what can I do for the following situation:
given a sentence set S and a query sentence q, find the closest match from S. The intuitive way is to pre-build a sentence embeddinds set for S and calculate Euclidean distance for each element in S with q. However, this might have bad performance since the big O is O(n * m) where n is the dimension of embeddings and m is the size of set S. I can use PCA to downgrade the dimension but I guess it's not a good way to do so. Any suggestion ?