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@ -103,7 +103,7 @@ namespace ZeroLevel.HNSW.Services.OPT
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/// <param name="q">query element</param>
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/// <param name="q">query element</param>
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/// <param name="ep">enter points ep</param>
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/// <param name="ep">enter points ep</param>
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/// <returns>Output: ef closest neighbors to q</returns>
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/// <returns>Output: ef closest neighbors to q</returns>
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internal void KNearestAtLayer(int entryPointId, Func<int, float> targetCosts, BinaryHeap W, int ef)
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internal IEnumerable<(int, float)> KNearestAtLayer(int entryPointId, Func<int, float> targetCosts, IEnumerable<(int, float)> w, int ef)
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{
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{
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/*
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/*
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* v ← ep // set of visited elements
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* v ← ep // set of visited elements
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@ -128,21 +128,25 @@ namespace ZeroLevel.HNSW.Services.OPT
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var v = new VisitedBitSet(_vectors.Count, _options.M);
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var v = new VisitedBitSet(_vectors.Count, _options.M);
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// v ← ep // set of visited elements
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// v ← ep // set of visited elements
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v.Add(entryPointId);
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v.Add(entryPointId);
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var W = new MaxHeap(ef + 1);
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foreach (var i in w) W.Push(i);
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var d = targetCosts(entryPointId);
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var d = targetCosts(entryPointId);
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// C ← ep // set of candidates
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// C ← ep // set of candidates
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var C = new BinaryHeap();
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var C = new MinHeap(ef);
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C.Push(entryPointId, d);
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C.Push((entryPointId, d));
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// W ← ep // dynamic list of found nearest neighbors
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// W ← ep // dynamic list of found nearest neighbors
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W.Push(entryPointId, d);
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W.Push((entryPointId, d));
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int farthestId;
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float farthestDistance;
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// run bfs
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// run bfs
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while (C.Count > 0)
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while (C.Count > 0)
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{
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{
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// get next candidate to check and expand
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// get next candidate to check and expand
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var toExpand = C.PopNearest();
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var toExpand = C.Pop();
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var farthestResult = W.Farthest;
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if (W.TryPeek(out _, out farthestDistance) && toExpand.Item2 > farthestDistance)
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if (toExpand.Item2 > farthestResult.Item2)
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{
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{
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// the closest candidate is farther than farthest result
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// the closest candidate is farther than farthest result
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break;
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break;
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@ -156,16 +160,17 @@ namespace ZeroLevel.HNSW.Services.OPT
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if (!v.Contains(neighbourId))
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if (!v.Contains(neighbourId))
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{
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{
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// enqueue perspective neighbours to expansion list
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// enqueue perspective neighbours to expansion list
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farthestResult = W.Farthest;
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W.TryPeek(out farthestId, out farthestDistance);
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var neighbourDistance = targetCosts(neighbourId);
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var neighbourDistance = targetCosts(neighbourId);
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if (W.Count < ef || neighbourDistance < farthestResult.Item2)
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if (W.Count < ef || (farthestId >= 0 && neighbourDistance < farthestDistance))
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{
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{
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C.Push(neighbourId, neighbourDistance);
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C.Push((neighbourId, neighbourDistance));
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W.Push(neighbourId, neighbourDistance);
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W.Push((neighbourId, neighbourDistance));
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if (W.Count > ef)
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if (W.Count > ef)
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{
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{
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W.PopFarthest();
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W.Pop();
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}
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}
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}
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}
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v.Add(neighbourId);
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v.Add(neighbourId);
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@ -174,6 +179,7 @@ namespace ZeroLevel.HNSW.Services.OPT
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}
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}
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C.Clear();
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C.Clear();
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v.Clear();
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v.Clear();
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return W;
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}
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}
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/// <summary>
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/// <summary>
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@ -182,7 +188,7 @@ namespace ZeroLevel.HNSW.Services.OPT
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/// <param name="q">query element</param>
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/// <param name="q">query element</param>
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/// <param name="ep">enter points ep</param>
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/// <param name="ep">enter points ep</param>
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/// <returns>Output: ef closest neighbors to q</returns>
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/// <returns>Output: ef closest neighbors to q</returns>
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internal void KNearestAtLayer(int entryPointId, Func<int, float> targetCosts, BinaryHeap W, int ef, SearchContext context)
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internal IEnumerable<(int, float)> KNearestAtLayer(int entryPointId, Func<int, float> targetCosts, IEnumerable<(int, float)> w, int ef, SearchContext context)
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{
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{
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/*
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/*
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* v ← ep // set of visited elements
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* v ← ep // set of visited elements
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@ -207,23 +213,28 @@ namespace ZeroLevel.HNSW.Services.OPT
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var v = new VisitedBitSet(_vectors.Count, _options.M);
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var v = new VisitedBitSet(_vectors.Count, _options.M);
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// v ← ep // set of visited elements
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// v ← ep // set of visited elements
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v.Add(entryPointId);
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v.Add(entryPointId);
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var W = new MaxHeap(ef + 1);
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foreach (var i in w) W.Push(i);
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// C ← ep // set of candidates
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// C ← ep // set of candidates
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var C = new BinaryHeap();
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var C = new MinHeap(ef);
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var d = targetCosts(entryPointId);
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var d = targetCosts(entryPointId);
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C.Push(entryPointId, d);
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C.Push((entryPointId, d));
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// W ← ep // dynamic list of found nearest neighbors
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// W ← ep // dynamic list of found nearest neighbors
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if (context.IsActiveNode(entryPointId))
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if (context.IsActiveNode(entryPointId))
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{
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{
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W.Push(entryPointId, d);
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W.Push((entryPointId, d));
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}
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}
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// run bfs
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// run bfs
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while (C.Count > 0)
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while (C.Count > 0)
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{
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{
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// get next candidate to check and expand
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// get next candidate to check and expand
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var toExpand = C.PopNearest();
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var toExpand = C.Pop();
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if (W.Count > 0)
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if (W.Count > 0)
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{
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{
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if (toExpand.Item2 > W.Farthest.Item2)
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if(W.TryPeek(out _, out var dist ))
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if (toExpand.Item2 > dist)
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{
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{
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// the closest candidate is farther than farthest result
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// the closest candidate is farther than farthest result
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break;
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break;
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@ -241,18 +252,18 @@ namespace ZeroLevel.HNSW.Services.OPT
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var neighbourDistance = targetCosts(neighbourId);
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var neighbourDistance = targetCosts(neighbourId);
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if (context.IsActiveNode(neighbourId))
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if (context.IsActiveNode(neighbourId))
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{
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{
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if (W.Count < ef || (W.Count > 0 && neighbourDistance < W.Farthest.Item2))
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if (W.Count < ef || (W.Count > 0 && (W.TryPeek(out _, out var dist) && neighbourDistance < dist)))
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{
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{
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W.Push(neighbourId, neighbourDistance);
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W.Push((neighbourId, neighbourDistance));
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if (W.Count > ef)
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if (W.Count > ef)
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{
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{
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W.PopFarthest();
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W.Pop();
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}
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}
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}
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}
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}
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}
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if (W.Count < ef)
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if (W.Count < ef)
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{
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{
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C.Push(neighbourId, neighbourDistance);
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C.Push((neighbourId, neighbourDistance));
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}
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}
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v.Add(neighbourId);
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v.Add(neighbourId);
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}
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}
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@ -260,6 +271,7 @@ namespace ZeroLevel.HNSW.Services.OPT
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}
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}
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C.Clear();
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C.Clear();
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v.Clear();
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v.Clear();
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return W;
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}
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}
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/// <summary>
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/// <summary>
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@ -268,7 +280,7 @@ namespace ZeroLevel.HNSW.Services.OPT
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/// <param name="q">query element</param>
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/// <param name="q">query element</param>
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/// <param name="ep">enter points ep</param>
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/// <param name="ep">enter points ep</param>
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/// <returns>Output: ef closest neighbors to q</returns>
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/// <returns>Output: ef closest neighbors to q</returns>
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internal void KNearestAtLayer(BinaryHeap W, int ef, SearchContext context)
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internal IEnumerable<(int, float)> KNearestAtLayer(IEnumerable<(int, float)> w, int ef, SearchContext context)
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{
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{
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/*
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/*
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* v ← ep // set of visited elements
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* v ← ep // set of visited elements
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@ -293,25 +305,28 @@ namespace ZeroLevel.HNSW.Services.OPT
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// v ← ep // set of visited elements
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// v ← ep // set of visited elements
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var v = new VisitedBitSet(_vectors.Count, _options.M);
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var v = new VisitedBitSet(_vectors.Count, _options.M);
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// C ← ep // set of candidates
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// C ← ep // set of candidates
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var C = new BinaryHeap();
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var C = new MinHeap(ef);
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foreach (var ep in context.EntryPoints)
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foreach (var ep in context.EntryPoints)
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{
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{
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var neighboursIds = GetNeighbors(ep).ToArray();
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var neighboursIds = GetNeighbors(ep).ToArray();
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for (int i = 0; i < neighboursIds.Length; ++i)
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for (int i = 0; i < neighboursIds.Length; ++i)
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{
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{
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C.Push(ep, _links.Distance(ep, neighboursIds[i]));
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C.Push((ep, _links.Distance(ep, neighboursIds[i])));
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}
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}
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v.Add(ep);
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v.Add(ep);
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}
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}
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// W ← ep // dynamic list of found nearest neighbors
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// W ← ep // dynamic list of found nearest neighbors
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var W = new MaxHeap(ef + 1);
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foreach (var i in w) W.Push(i);
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// run bfs
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// run bfs
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while (C.Count > 0)
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while (C.Count > 0)
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{
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{
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// get next candidate to check and expand
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// get next candidate to check and expand
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var toExpand = C.PopNearest();
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var toExpand = C.Pop();
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if (W.Count > 0)
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if (W.Count > 0)
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{
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{
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if (toExpand.Item2 > W.Farthest.Item2)
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if (W.TryPeek(out _, out var dist) && toExpand.Item2 > dist)
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{
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{
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// the closest candidate is farther than farthest result
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// the closest candidate is farther than farthest result
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break;
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break;
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@ -319,12 +334,12 @@ namespace ZeroLevel.HNSW.Services.OPT
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}
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}
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if (context.IsActiveNode(toExpand.Item1))
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if (context.IsActiveNode(toExpand.Item1))
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{
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{
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if (W.Count < ef || W.Count == 0 || (W.Count > 0 && toExpand.Item2 < W.Farthest.Item2))
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if (W.Count < ef || W.Count == 0 || (W.Count > 0 && (W.TryPeek(out _, out var dist) && toExpand.Item2 < dist)))
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{
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{
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W.Push(toExpand.Item1, toExpand.Item2);
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W.Push((toExpand.Item1, toExpand.Item2));
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if (W.Count > ef)
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if (W.Count > ef)
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{
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{
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W.PopFarthest();
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W.Pop();
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}
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}
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}
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}
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}
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}
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@ -333,21 +348,21 @@ namespace ZeroLevel.HNSW.Services.OPT
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{
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{
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while (W.Count > ef)
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while (W.Count > ef)
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{
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{
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W.PopFarthest();
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W.Pop();
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}
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}
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return;
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return W;
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}
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}
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else
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else
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{
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{
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foreach (var c in W)
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foreach (var c in W)
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{
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{
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C.Push(c.Item1, c.Item2);
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C.Push((c.Item1, c.Item2));
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}
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}
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}
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}
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while (C.Count > 0)
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while (C.Count > 0)
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{
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{
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// get next candidate to check and expand
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// get next candidate to check and expand
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var toExpand = C.PopNearest();
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var toExpand = C.Pop();
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// expand candidate
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// expand candidate
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var neighboursIds = GetNeighbors(toExpand.Item1).ToArray();
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var neighboursIds = GetNeighbors(toExpand.Item1).ToArray();
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for (int i = 0; i < neighboursIds.Length; ++i)
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for (int i = 0; i < neighboursIds.Length; ++i)
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@ -359,18 +374,18 @@ namespace ZeroLevel.HNSW.Services.OPT
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var neighbourDistance = _links.Distance(toExpand.Item1, neighbourId);
|
|
|
|
var neighbourDistance = _links.Distance(toExpand.Item1, neighbourId);
|
|
|
|
if (context.IsActiveNode(neighbourId))
|
|
|
|
if (context.IsActiveNode(neighbourId))
|
|
|
|
{
|
|
|
|
{
|
|
|
|
if (W.Count < ef || (W.Count > 0 && neighbourDistance < W.Farthest.Item2))
|
|
|
|
if (W.Count < ef || (W.Count > 0 && (W.TryPeek(out _, out var dist) && neighbourDistance < dist)))
|
|
|
|
{
|
|
|
|
{
|
|
|
|
W.Push(neighbourId, neighbourDistance);
|
|
|
|
W.Push((neighbourId, neighbourDistance));
|
|
|
|
if (W.Count > ef)
|
|
|
|
if (W.Count > ef)
|
|
|
|
{
|
|
|
|
{
|
|
|
|
W.PopFarthest();
|
|
|
|
W.Pop();
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
if (W.Count < ef)
|
|
|
|
if (W.Count < ef)
|
|
|
|
{
|
|
|
|
{
|
|
|
|
C.Push(neighbourId, neighbourDistance);
|
|
|
|
C.Push((neighbourId, neighbourDistance));
|
|
|
|
}
|
|
|
|
}
|
|
|
|
v.Add(neighbourId);
|
|
|
|
v.Add(neighbourId);
|
|
|
|
}
|
|
|
|
}
|
|
|
@ -378,19 +393,22 @@ namespace ZeroLevel.HNSW.Services.OPT
|
|
|
|
}
|
|
|
|
}
|
|
|
|
C.Clear();
|
|
|
|
C.Clear();
|
|
|
|
v.Clear();
|
|
|
|
v.Clear();
|
|
|
|
|
|
|
|
return W;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
/// <summary>
|
|
|
|
/// Algorithm 3
|
|
|
|
/// Algorithm 3
|
|
|
|
/// </summary>
|
|
|
|
/// </summary>
|
|
|
|
internal BinaryHeap SELECT_NEIGHBORS_SIMPLE(BinaryHeap W, int M)
|
|
|
|
internal MaxHeap SELECT_NEIGHBORS_SIMPLE(IEnumerable<(int, float)> w, int M)
|
|
|
|
{
|
|
|
|
{
|
|
|
|
|
|
|
|
var W = new MaxHeap(w.Count());
|
|
|
|
|
|
|
|
foreach (var i in w) W.Push(i);
|
|
|
|
var bestN = M;
|
|
|
|
var bestN = M;
|
|
|
|
if (W.Count > bestN)
|
|
|
|
if (W.Count > bestN)
|
|
|
|
{
|
|
|
|
{
|
|
|
|
while (W.Count > bestN)
|
|
|
|
while (W.Count > bestN)
|
|
|
|
{
|
|
|
|
{
|
|
|
|
W.PopFarthest();
|
|
|
|
W.Pop();
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
return W;
|
|
|
|
return W;
|
|
|
@ -406,11 +424,13 @@ namespace ZeroLevel.HNSW.Services.OPT
|
|
|
|
/// <param name="extendCandidates">flag indicating whether or not to extend candidate list</param>
|
|
|
|
/// <param name="extendCandidates">flag indicating whether or not to extend candidate list</param>
|
|
|
|
/// <param name="keepPrunedConnections">flag indicating whether or not to add discarded elements</param>
|
|
|
|
/// <param name="keepPrunedConnections">flag indicating whether or not to add discarded elements</param>
|
|
|
|
/// <returns>Output: M elements selected by the heuristic</returns>
|
|
|
|
/// <returns>Output: M elements selected by the heuristic</returns>
|
|
|
|
internal BinaryHeap SELECT_NEIGHBORS_HEURISTIC(Func<int, float> distance, BinaryHeap W, int M)
|
|
|
|
internal MaxHeap SELECT_NEIGHBORS_HEURISTIC(Func<int, float> distance, IEnumerable<(int, float)> w, int M)
|
|
|
|
{
|
|
|
|
{
|
|
|
|
// R ← ∅
|
|
|
|
// R ← ∅
|
|
|
|
var R = new BinaryHeap();
|
|
|
|
var R = new MaxHeap(_options.EFConstruction);
|
|
|
|
// W ← C // working queue for the candidates
|
|
|
|
// W ← C // working queue for the candidates
|
|
|
|
|
|
|
|
var W = new MaxHeap(_options.EFConstruction + 1);
|
|
|
|
|
|
|
|
foreach (var i in w) W.Push(i);
|
|
|
|
// if extendCandidates // extend candidates by their neighbors
|
|
|
|
// if extendCandidates // extend candidates by their neighbors
|
|
|
|
if (_options.ExpandBestSelection)
|
|
|
|
if (_options.ExpandBestSelection)
|
|
|
|
{
|
|
|
|
{
|
|
|
@ -432,30 +452,30 @@ namespace ZeroLevel.HNSW.Services.OPT
|
|
|
|
// W ← W ⋃ eadj
|
|
|
|
// W ← W ⋃ eadj
|
|
|
|
foreach (var id in extendBuffer)
|
|
|
|
foreach (var id in extendBuffer)
|
|
|
|
{
|
|
|
|
{
|
|
|
|
W.Push(id, distance(id));
|
|
|
|
W.Push((id, distance(id)));
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
// Wd ← ∅ // queue for the discarded candidates
|
|
|
|
// Wd ← ∅ // queue for the discarded candidates
|
|
|
|
var Wd = new BinaryHeap();
|
|
|
|
var Wd = new MinHeap(_options.EFConstruction);
|
|
|
|
// while │W│ > 0 and │R│< M
|
|
|
|
// while │W│ > 0 and │R│< M
|
|
|
|
while (W.Count > 0 && R.Count < M)
|
|
|
|
while (W.Count > 0 && R.Count < M)
|
|
|
|
{
|
|
|
|
{
|
|
|
|
// e ← extract nearest element from W to q
|
|
|
|
// e ← extract nearest element from W to q
|
|
|
|
var (e, ed) = W.PopNearest();
|
|
|
|
var (e, ed) = W.Pop();
|
|
|
|
var (fe, fd) = R.PopFarthest();
|
|
|
|
var (fe, fd) = R.Pop();
|
|
|
|
|
|
|
|
|
|
|
|
// if e is closer to q compared to any element from R
|
|
|
|
// if e is closer to q compared to any element from R
|
|
|
|
if (R.Count == 0 ||
|
|
|
|
if (R.Count == 0 ||
|
|
|
|
ed < fd)
|
|
|
|
ed < fd)
|
|
|
|
{
|
|
|
|
{
|
|
|
|
// R ← R ⋃ e
|
|
|
|
// R ← R ⋃ e
|
|
|
|
R.Push(e, ed);
|
|
|
|
R.Push((e, ed));
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
else
|
|
|
|
{
|
|
|
|
{
|
|
|
|
// Wd ← Wd ⋃ e
|
|
|
|
// Wd ← Wd ⋃ e
|
|
|
|
Wd.Push(e, ed);
|
|
|
|
Wd.Push((e, ed));
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
// if keepPrunedConnections // add some of the discarded // connections from Wd
|
|
|
|
// if keepPrunedConnections // add some of the discarded // connections from Wd
|
|
|
@ -465,8 +485,8 @@ namespace ZeroLevel.HNSW.Services.OPT
|
|
|
|
while (Wd.Count > 0 && R.Count < M)
|
|
|
|
while (Wd.Count > 0 && R.Count < M)
|
|
|
|
{
|
|
|
|
{
|
|
|
|
// R ← R ⋃ extract nearest element from Wd to q
|
|
|
|
// R ← R ⋃ extract nearest element from Wd to q
|
|
|
|
var nearest = Wd.PopNearest();
|
|
|
|
var nearest = Wd.Pop();
|
|
|
|
R.Push(nearest.Item1, nearest.Item2);
|
|
|
|
R.Push((nearest.Item1, nearest.Item2));
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
// return R
|
|
|
|
// return R
|
|
|
|