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<!DOCTYPE html>
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<title>Neo4J A* search</title>
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<h2 class="center" id="title">NEO4J A* SEARCH</h2>
<h6 class="center">14 SEPTEMBER 2025</h5>
<br>
<div class="threecol justify"><p>Back in 2018, we used the <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.
Performance issues with Neo4J’s then-available shortest-path algorithms limited
our search to about 4,000 route points.</p>
<p>The fix led to my first contribution to an open-source project:</p>
<div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>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;
}
}
}
</code></pre></div></div>
<p>If you are new to them, a graph is a finite set of vertices (such as ports
ships are known to travel through), and a subset of vertex pairs (such as
origin and destination ports) known as edges.</p>
<p>Edges can have weights. In the case of ships and ports, the weights could be
the distances between ports. For various 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.</p>
<p>There’s nothing spectacular about the code. It is, for the most part, a patch
over Dijkstra’s algorithm that employs spherical distance between vertices as a
heuristic to steer the search in the right direction. Dijkstra’s algorithm, on
the other hand, explores all possible paths from the source, which is what
makes it slower.</p>
<p>The heuristic function is domain-specific. I planned to make it configurable,
but didn’t get around to it. With the help of my A* algorithm, we scaled our
search to include all the route points of interest. <a href="https://github.com/neo4j-contrib/neo4j-graph-algorithms/releases/tag/3.4.0.0" class="external" target="_blank" rel="noopener noreferrer">Here’s</a> a link to
the now-archived official release.</p>
</div>
<p class="post-author right italics">by Wickramage Don Sadeep Madurange</p>
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