NEO4J A* SEARCH
14 SEPTEMBER 2025
Back in 2018, we used the Neo4J 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.
Performance issues with Neo4J’s shortest-path algorithms limited our search to
about 4,000 route points.
A graph is a finite set of vertices, and a subset of vertex pairs known as
edges. Edges can have weights.
In the case of vessel tracking, the route points can be modeled as a graph
with the distances between them as 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.
Dijkstra’s algorithm is one such algorithm that finds the shortest path between
two vertices. The one drawback of this algorithm is that it computes all the
shortest paths from the source to all other vertices before terminating at the
destination vertex.
The following enhancement, also known as the A* search, employs spherical
distance between route points (which are on the earth’s surface) as a heuristic
to steer the search in the direction of the destination far more quickly:
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 Neo4J graph algorithms open-source project v3.4 shipped
with my implementation of the A* search algorithm.
Back in 2018, we used the Neo4J 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. Performance issues with Neo4J’s shortest-path algorithms limited our search to about 4,000 route points.
A graph is a finite set of vertices, and a subset of vertex pairs known as edges. Edges can have weights.
In the case of vessel tracking, the route points can be modeled as a graph with the distances between them as 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.
Dijkstra’s algorithm is one such algorithm that finds the shortest path between two vertices. The one drawback of this algorithm is that it computes all the shortest paths from the source to all other vertices before terminating at the destination vertex.
The following enhancement, also known as the A* search, employs spherical distance between route points (which are on the earth’s surface) as a heuristic to steer the search in the direction of the destination far more quickly:
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 Neo4J graph algorithms open-source project v3.4 shipped with my implementation of the A* search algorithm.