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----
-title: Neo4J A* search
-date: 2025-09-14
-layout: post
----
-
-Back in 2018, we used <a href="https://neo4j.com/" class="external"
-target="_blank" rel="noopener noreferrer">Neo4J</a> graph database to track the
-movement of marine vessels. We were interested in the shortest path a ship
-could take through a network of about 13,000 route points. Algorithms based on
-graph theory, such as A* search, provide optimal solutions to such problems.
-In other words, the set of route points lends itself well to a model based on
-graphs.
-
-A graph is a finite set of vertices, and a subset of vertex pairs (edges).
-Edges can have weights. In the case of vessel tracking, the route points form
-the vertices of a graph; the routes between them, the edges; and the distances
-between them are the weights. For different reasons, people are interested in
-minimizing (or maximizing) the weight of a path through a set of vertices. For
-instance, we may want to find the shortest path between two ports.
-
-Given such a graph, an algorithm like Dijkstra's search could compute the
-shortest path between two vertices. In fact, this was the algorithm Neo4J
-shipped with at the time. One drawback of Dijkstra's algorithm is that it
-computes all the shortest paths from the source to all other vertices before
-terminating at the destination vertex. The exhaustive nature of this search
-limited our search to about 4,000 route points.
-
-The following enhancement to Dijkstra's search, also known as the A* search,
-employs a heuristic to steer the search in the direction of the destination
-more quickly. In the case of our network of vessels, which are on the earth's
-surface, spherical distance is a good candidate for a heuristic:
-
-```
-package org.neo4j.graphalgo.impl;
-
-import java.util.stream.Stream;
-import java.util.stream.StreamSupport;
-
-import org.neo4j.graphalgo.api.Graph;
-import org.neo4j.graphalgo.core.utils.ProgressLogger;
-import org.neo4j.graphalgo.core.utils.queue.IntPriorityQueue;
-import org.neo4j.graphalgo.core.utils.queue.SharedIntPriorityQueue;
-import org.neo4j.graphalgo.core.utils.traverse.SimpleBitSet;
-import org.neo4j.graphdb.Direction;
-import org.neo4j.graphdb.Node;
-import org.neo4j.kernel.internal.GraphDatabaseAPI;
-
-import com.carrotsearch.hppc.IntArrayDeque;
-import com.carrotsearch.hppc.IntDoubleMap;
-import com.carrotsearch.hppc.IntDoubleScatterMap;
-import com.carrotsearch.hppc.IntIntMap;
-import com.carrotsearch.hppc.IntIntScatterMap;
-
-public class ShortestPathAStar extends Algorithm<ShortestPathAStar> {
-    
-    private final GraphDatabaseAPI dbService;
-    private static final int PATH_END = -1;
-    
-    private Graph graph;
-    private final int nodeCount;
-    private IntDoubleMap gCosts;
-    private IntDoubleMap fCosts;
-    private double totalCost;
-    private IntPriorityQueue openNodes;
-    private IntIntMap path;
-    private IntArrayDeque shortestPath;
-    private SimpleBitSet closedNodes;
-    private final ProgressLogger progressLogger;
-    
-    public static final double NO_PATH_FOUND = -1.0;
-    
-    public ShortestPathAStar(
-        final Graph graph,
-        final GraphDatabaseAPI dbService) {
-
-        this.graph = graph;
-        this.dbService = dbService;
-
-        nodeCount = Math.toIntExact(graph.nodeCount());
-        gCosts = new IntDoubleScatterMap(nodeCount);
-        fCosts = new IntDoubleScatterMap(nodeCount);
-        openNodes = SharedIntPriorityQueue.min(
-            nodeCount,
-            fCosts,
-            Double.MAX_VALUE);
-        path = new IntIntScatterMap(nodeCount);
-        closedNodes = new SimpleBitSet(nodeCount);
-        shortestPath = new IntArrayDeque();
-        progressLogger = getProgressLogger();
-    }
-    
-    public ShortestPathAStar compute(
-        final long startNode,
-        final long goalNode,
-        final String propertyKeyLat,
-        final String propertyKeyLon,
-        final Direction direction) {
-
-        reset();
-
-        final int startNodeInternal = 
-            graph.toMappedNodeId(startNode);
-        final double startNodeLat =
-            getNodeCoordinate(startNodeInternal, propertyKeyLat);
-        final double startNodeLon = 
-            getNodeCoordinate(startNodeInternal, propertyKeyLon);
-
-        final int goalNodeInternal =
-            graph.toMappedNodeId(goalNode);
-        final double goalNodeLat = 
-            getNodeCoordinate(goalNodeInternal, propertyKeyLat);
-        final double goalNodeLon = 
-            getNodeCoordinate(goalNodeInternal, propertyKeyLon);
-
-        final double initialHeuristic = 
-            computeHeuristic(startNodeLat,
-                startNodeLon,
-                goalNodeLat,
-                goalNodeLon);
-
-        gCosts.put(startNodeInternal, 0.0);
-        fCosts.put(startNodeInternal, initialHeuristic);
-        openNodes.add(startNodeInternal, 0.0);
-
-        run(goalNodeInternal,
-            propertyKeyLat,
-            propertyKeyLon,
-            direction);
-
-        if (path.containsKey(goalNodeInternal)) {
-            totalCost = gCosts.get(goalNodeInternal);
-            int node = goalNodeInternal;
-            while (node != PATH_END) {
-                shortestPath.addFirst(node);
-                node = path.getOrDefault(node, PATH_END);
-            }
-        }
-        return this;
-    }
-    
-    private void run(
-        final int goalNodeId,
-        final String propertyKeyLat,
-        final String propertyKeyLon,
-        final Direction direction) {
-
-        final double goalLat = 
-            getNodeCoordinate(goalNodeId, propertyKeyLat);
-        final double goalLon =
-            getNodeCoordinate(goalNodeId, propertyKeyLon);
-
-        while (!openNodes.isEmpty() && running()) {
-            int currentNodeId = openNodes.pop();
-            if (currentNodeId == goalNodeId) {
-                return;
-            }
-
-            closedNodes.put(currentNodeId);
-
-            double currentNodeCost = 
-                this.gCosts.getOrDefault(
-                    currentNodeId, 
-                    Double.MAX_VALUE);
-
-            graph.forEachRelationship(
-                currentNodeId,
-                direction,
-                (source, target, relationshipId, weight) -> {
-                    double neighbourLat = 
-                        getNodeCoordinate(target, propertyKeyLat);
-                    double neighbourLon = 
-                        getNodeCoordinate(target, propertyKeyLon);
-                    double heuristic = 
-                        computeHeuristic(
-                            neighbourLat, 
-                            neighbourLon, 
-                            goalLat,
-                            goalLon);
-
-                    updateCosts(
-                        source,
-                        target,
-                        weight + currentNodeCost,
-                        heuristic);
-
-                    if (!closedNodes.contains(target)) {
-                        openNodes.add(target, 0);
-                    }
-                    return true;
-                });
-
-            progressLogger.logProgress(
-                (double) currentNodeId / (nodeCount - 1));
-        }
-    }
-    
-    private double computeHeuristic(
-        final double lat1,
-        final double lon1,
-        final double lat2,
-        final double lon2) {
-
-        final int earthRadius = 6371;
-        final double kmToNM = 0.539957;
-        final double latDistance = Math.toRadians(lat2 - lat1);
-        final double lonDistance = Math.toRadians(lon2 - lon1);
-        final double a = Math.sin(latDistance / 2)
-            * Math.sin(latDistance / 2)
-            + Math.cos(Math.toRadians(lat1))
-            * Math.cos(Math.toRadians(lat2))
-            * Math.sin(lonDistance / 2)
-            * Math.sin(lonDistance / 2);
-        final double c = 2
-            * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
-        final double distance = earthRadius * c * kmToNM;
-        return distance;
-    }
-    
-    private double getNodeCoordinate(
-        final int nodeId,
-        final String coordinateType) {
-
-        final long neo4jId = graph.toOriginalNodeId(nodeId);
-        final Node node = dbService.getNodeById(neo4jId);
-        return (double) node.getProperty(coordinateType);
-    }
-    
-    private void updateCosts(
-        final int source, 
-        final int target, 
-        final double newCost,
-        final double heuristic) {
-
-        final double oldCost = 
-            gCosts.getOrDefault(target, Double.MAX_VALUE);
-
-        if (newCost < oldCost) {
-            gCosts.put(target, newCost);
-            fCosts.put(target, newCost + heuristic);
-            path.put(target, source);
-        }
-    }
-    
-    private void reset() {
-        closedNodes.clear();
-        openNodes.clear();
-        gCosts.clear();
-        fCosts.clear();
-        path.clear();
-        shortestPath.clear();
-        totalCost = NO_PATH_FOUND;
-    }
-    
-    public Stream<Result> resultStream() {
-        return StreamSupport.stream(
-            shortestPath.spliterator(), false)
-                .map(cursor -> new Result(
-                    graph.toOriginalNodeId(cursor.value),
-                    gCosts.get(cursor.value)));
-    }
-
-    public IntArrayDeque getFinalPath() {
-        return shortestPath;
-    }
-    
-    public double getTotalCost() {
-        return totalCost;
-    }
-
-    public int getPathLength() {
-        return shortestPath.size();
-    }
-    
-    @Override
-    public ShortestPathAStar me() {
-        return this;
-    }
-
-    @Override
-    public ShortestPathAStar release() {
-        graph = null;
-        gCosts = null;
-        fCosts = null;
-        openNodes = null;
-        path = null;
-        shortestPath = null;
-        closedNodes = null;
-        return this;
-    }
-    
-    public static class Result {
-
-        /**
-         * the neo4j node id
-         */
-        public final Long nodeId;
-
-        /**
-         * cost to reach the node from startNode
-         */
-        public final Double cost;
-
-        public Result(Long nodeId, Double cost) {
-            this.nodeId = nodeId;
-            this.cost = cost;
-        }
-    }
-}
-```
-
-The heuristic function is domain-specific. If chosen wisely, it can
-significantly speed up the search. In our case, we achieved a 300x speedup,
-enabling us to expand our search from 4,000 to 13,000 route points. The <a
-href="https://github.com/neo4j-contrib/neo4j-graph-algorithms/releases/tag/3.4.0.0"
-class="external" target="_blank" rel="noopener noreferrer">v3.4.0</a> of the
-Neo4J graph algorithms shipped with the A* search algorithm.
-