Update ACORN filtering optimization section in efficient filtering. (opensearch-project#10698)

* Update ACORN filtering optimiztaion section in efficient filtering.

Signed-off-by: Dooyong Kim <[email protected]>

* Apply suggestions from code review

Signed-off-by: Nathan Bower <[email protected]>

---------

Signed-off-by: Dooyong Kim <[email protected]>
Signed-off-by: Nathan Bower <[email protected]>
Co-authored-by: Dooyong Kim <[email protected]>
Co-authored-by: Nathan Bower <[email protected]>

Author: 2 people

_vector-search/filter-search-knn/efficient-knn-filtering.md

@@ -402,6 +402,15 @@ The response returns the two matching documents:
 
 For more ways to construct a filter, see [Constructing a filter](#constructing-a-filter).
 
+### ACORN filtering optimization
+Introduced 3.1
+{: .label .label-purple }
+The ACORN filtering optimization modifies the baseline algorithm to score and explore only vectors that match the filtering criteria. When filtering increases graph sparsity, the search expands to include neighbors of neighbors. The extent of this additional exploration depends on the percentage of neighbors filtered out, with more restrictive filters resulting in a wider search.
+
+The algorithm bypasses these optimizations entirely when filtering is minimal. By default, this threshold is 60%. Extended neighbor exploration occurs only if fewer than 90% of the current neighbors match the filter. 
+
+When [memory-optimized search]({{site.url}}{{site.baseurl}}/vector-search/optimizing-storage/memory-optimized-search/) is enabled, the efficient filter framework continues to apply filtering within HNSW. The ACORN filtering optimization is applied only when the number of filtered documents is 60% or fewer of the total number of documents in the current search space being considered by the HNSW algorithm.
+
 ## Constructing a filter
 
 There are multiple ways to construct a filter for the same condition. For example, you can use the following constructs to create a filter that returns hotels that provide parking:

_vector-search/filter-search-knn/index.md

@@ -14,7 +14,8 @@ To refine vector search results, you can filter a vector search using one of the
 
 - [Efficient k-nearest neighbors (k-NN) filtering]({{site.url}}{{site.baseurl}}/vector-search/filter-search-knn/efficient-knn-filtering/): This approach applies filtering _during_ the vector search, as opposed to before or after the vector search, which ensures that `k` results are returned (if there are at least `k` results in total). This approach is supported by the following engines:
   - Lucene engine with a Hierarchical Navigable Small World (HNSW) algorithm (OpenSearch version 2.4 and later) 
-  - Faiss engine with an HNSW algorithm (OpenSearch version 2.9 and later) or IVF algorithm (OpenSearch version 2.10 and later)
+  - Faiss engine with an HNSW algorithm (OpenSearch version 2.9 and later) or IVF algorithm (OpenSearch version 2.10 and later). In OpenSearch version 3.1 and later, when using the Faiss engine and HNSW, the [Lucene ACORN filtering optimization](https://github.com/apache/lucene/pull/14160) is applied during HNSW traversal when [memory-optimized search]({{site.url}}{{site.baseurl}}/vector-search/optimizing-storage/memory-optimized-search/) is enabled.
+    - With the Faiss engine and HNSW, the [Lucene ACORN filtering optimization](https://github.com/apache/lucene/pull/14160) is applied during HNSW traversal when [memory-optimized search]({{site.url}}{{site.baseurl}}/vector-search/optimizing-storage/memory-optimized-search/) is enabled.
 
 -  [Post-filtering]({{site.url}}{{site.baseurl}}/vector-search/filter-search-knn/post-filtering/): Because it is performed after the vector search, this approach may return significantly fewer than `k` results for a restrictive filter. You can use the following two filtering strategies for this approach:
     - [Boolean post-filter]({{site.url}}{{site.baseurl}}/vector-search/filter-search-knn/post-filtering/#boolean-filter-with-ann-search): This approach runs an [approximate nearest neighbor (ANN)]({{site.url}}{{site.baseurl}}/search-plugins/knn/approximate-knn/) search and then applies a filter to the results. The two query parts are executed independently, and then the results are combined based on the query operator (`should`, `must`, and so on) provided in the query.