diff --git a/tests/utils/partition_hmetis.cpp b/tests/utils/partition_hmetis.cpp
index db1ad7272..4db1d0284 100644
--- a/tests/utils/partition_hmetis.cpp
+++ b/tests/utils/partition_hmetis.cpp
@@ -378,7 +378,7 @@ int aux_main(const std::string &input_file,
             std::make_unique<float[]>(num_shards * num_subcentroids * dim);
         std::unique_ptr<uint32_t[]> closest_centers_ivf =
             std::make_unique<uint32_t[]>(num_shards * num_subcentroids);
-        // for each shard centers, find the `num_subcentroids` many closest shard centers
+        // for each shard center, find the `num_subcentroids` many closest shard centers
         // (including itself, which will be the closest)
         math_utils::compute_closest_centers(
             centroids.get(), num_shards, dim, centroids.get(), num_shards,
@@ -493,7 +493,7 @@ int aux_main(const std::string &input_file,
       } else if (mode == "multicentroids" || mode == "multicentroids-random" ||
                  mode == "multicentroids-neighbors") {
 
-        constexpr int submode = 1;
+        constexpr int submode = 3;
 
         std::unique_ptr<float[]> queries_float =
             std::make_unique<float[]>(num_queries * dim);
@@ -531,7 +531,7 @@ int aux_main(const std::string &input_file,
               // compute score of shard_id for query_id
               float score = 0.0;
               for (int i = 0; i < num_subcentroids; ++i) {
-                const float dist = sqrt(math_utils::calc_distance(
+                const float    dist = sqrt(math_utils::calc_distance(
                     queries_float.get() + query_id * dim,
                     subcentroids.get() + shard_id * num_subcentroids * dim +
                         i * dim,
@@ -552,6 +552,62 @@ int aux_main(const std::string &input_file,
               // wasn't present
             }
           }
+        } else if (submode == 3) {
+          if (mode != "subcentroids_random") {
+			diskann::cout << "Error: submode 3 only works with "
+							 "multicentroids-random"
+						  << std::endl;
+			return -1;
+		  }
+          // 3: Depends on a specific K.
+          // For each query,
+          // we add the subsampled points one by one, from the closest to the farthest.
+          // As we do this, we maintain for each shard a `worth` value:
+          // the expected number of points at distance <= d = current distance
+          // (thought of as the GT points) that are in this shard.
+          // Worth is computed as: (number of subsampled points from this shard seen so far)
+          // * (shard size) / num_subcentroids.
+          // We stop once the sum of worths of all shards is >= K
+          // (at this point we estimate that we have seen all the subsampled GT points).
+          // Then we sort the shards by worth (and later take the top query_fanout shards).
+
+
+          const size_t num_subcenters = num_shards * num_subcentroids;
+          std::unique_ptr<uint32_t[]> closest_centroids_ivf =
+              std::make_unique<uint32_t[]>(num_queries * num_subcenters);
+          math_utils::compute_closest_centers(
+              queries_float.get(), num_queries, dim, subcentroids.get(),
+              num_subcenters, num_subcenters, closest_centroids_ivf.get());
+          for (size_t query_id = 0; query_id < num_queries; ++query_id) {
+              std::vector<float> worth_of_shard(num_shards, 0.0);
+              float              sum_of_worths = 0.0;
+              for (int i = 0; i < num_subcenters; ++i) {
+                const size_t shard_id =
+				  closest_centroids_ivf[query_id * num_subcenters + i] /
+				  num_subcentroids;
+                const float worth_increase =
+                  points_routed_to_shard[shard_id].size() * 1.0 / num_subcentroids;
+				worth_of_shard[shard_id] += worth_increase;
+                sum_of_worths += worth_increase;
+                if (sum_of_worths >= K) {
+				  break;
+				}
+              }
+              std::vector<std::pair<float, size_t>> shards_with_worths;
+              for (size_t shard_id = 0; shard_id < num_shards; ++shard_id) {
+                shards_with_worths.emplace_back(-worth_of_shard[shard_id],
+                                                shard_id);
+			  }
+              sort(shards_with_worths.begin(), shards_with_worths.end());
+              query_to_shards.emplace_back();
+              for (int i = 0; i < num_shards; ++i) {
+				const size_t shard_id = shards_with_worths[i].second;
+                query_to_shards[query_id].emplace_back(
+					shard_id, shard_to_count_of_GT_pts[query_id][shard_id]);
+				// shard_to_count_of_GT_pts[query_id][shard_id] will be(come) 0 if
+				// wasn't present
+			  }
+          }
         } else {
           diskann::cout << "what submode?" << std::endl;
           return -1;