Hierarchical Navigable Small Worlds(zilliz.com)

    nns = [best]
    visit = set(best)  # set of visited nodes
    candid = [best]  # candidate nodes to insert into nearest neighbors

    # find top-k nearest neighbors
    while candid:
        cv = heappop(candid)

        if nns[-1][0] < cv[0]:
            break

        # loop through all nearest neighbors to the candidate vector
        for e in graph[cv[1]][1]:
            d = np.linalg.norm(graph[e][0] - query)
            if (d, e) not in visit:
                visit.add((d, e))

                # push only "better" vectors into candidate heap
                if d < nns[-1][0] or len(nns) < ef:
                    heappush(candid, (d, e))
                    insort(nns, (d, e))
                    if len(nns) > ef:
                        nns.pop()

    nearest_neighbors = [best]
    visited = set(best)
    candidates = [best]

    # find top-k nearest neighbors
    while candidates:
        candidate_vector = heappop(candidates)

        if nearest_neighbors[-1][0] < candidate_vector[0]:
            break

        # loop through all nearest neighbors to the candidate vector
        for neighbor in graph[candidate_vector[1]][1]:
            distance = np.linalg.norm(graph[e][0] - query)

            if (distance, neighbor) in visit:
                continue

            visited.add((distance, neighbor))

            # push only "better" vectors into candidate heap
            if distance < nearest_neighbors[-1][0] or len(nearest_neighbors) < epsilon:
               heappush(candidates, (distance, neighbor))
               insort(nns, (distance, neighbor))
               if len(nearest_neighbors) > epsilon:
                   nearest_neighbors.pop()