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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="twocol justify"><p>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 an optimal solution to this
problem. Therefore, it was useful to model the set of route points as a graph.</p>
<p>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.</p>
<p>Given such a graph, an algorithm like Dijkstra’s search could compute the
shortest path between two vertices. In fact, this was the algorithm the Neo4J
project 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.</p>
<p>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:</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>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.</p>
</div>
<p class="post-author right">by Wickramage Don Sadeep Madurange</p>
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