Working range query

index.js

@@ -1,35 +1,44 @@
 const express = require('express');
 const bodyParser = require('body-parser');
 const MTree = require('./m-tree/mtree');
-const dimensions = 2;
+const dimensions = 3;
 
+// Generator used to generate random points for the MTree
 const Generator = require('./data/generator');
 
+// Express app
 const app = express();
 app.use(bodyParser.json());
 
-
+// Euclidean distance function used as the distance metric for the MTree
 function euclideanDistance(a, b) {
     return Math.sqrt(a.reduce((acc, val, i) => acc + (val - b[i]) ** 2, 0));
 }
-const mtree = new MTree(dimensions, 10, euclideanDistance);
 
+// Create an MTree with the given dimensions and capacity, using the Euclidean distance
+const mtree = new MTree(dimensions, 6, euclideanDistance);
+
+// Generate 1000 random points
 const generator = new Generator(dimensions);
-const points = generator.generateMany(1000);
+const points = generator.generateMany(100);
 let i = 0;
+// Insert all points into the MTree
 points.forEach(point => { mtree.insert(point); i++; console.log(i); });
 
+// Serve the index.html file
 app.get('/', (req, res) => {
     res.sendFile(__dirname + '/index.html');
 });
 
+// Return the MTree
 app.get('/tree', (req, res) => {
     res.send(JSON.parse(JSON.stringify(mtree, (key, value) => {
-        if (key === 'parent') return value && value.id;
+        if (key === 'parent' || key === 'mtree') return value && value.id;
         return value;
     })));
 });
 
+// Insert a point into the MTree
 app.post('/insert', (req, res) => {
     const point = req.body.point;
     if (!point || !Array.isArray(point)) {
@@ -39,15 +48,21 @@ app.post('/insert', (req, res) => {
     res.send('Point inserted');
 });
 
+// Perform a range query on the MTree
 app.get('/rangeQuery', (req, res) => {
     const { queryPoint, radius } = req.query;
     if (!queryPoint || !radius) {
         return res.status(400).send('Invalid query parameters');
     }
     const result = mtree.rangeQuery(JSON.parse(queryPoint), parseFloat(radius));
+
+    const sequentialResult = points.filter(point => euclideanDistance(point, JSON.parse(queryPoint)) <= parseFloat(radius));
+    console.log(sequentialResult);
+
     res.send(result);
 });
 
+// Perform a k-NN query on the MTree
 app.get('/kNNQuery', (req, res) => {
     const { queryPoint, k } = req.query;
     if (!queryPoint || !k) {
@@ -57,11 +72,13 @@ app.get('/kNNQuery', (req, res) => {
     res.send(result);
 });
 
+// Start the server
 app.listen(3000, () => {
     console.log('MTree API is running on port 3000');
     //console.log(mtree);
 });
 
+// Recreate the MTree with the given dimensions
 app.post('/recreate', (req, res) => {
     const { dimensions } = req.body;
     if (!dimensions || typeof dimensions !== 'number') {
@@ -72,3 +89,4 @@ app.post('/recreate', (req, res) => {
     points.forEach(point => mtree.insert(point));
     res.send('MTree recreated');
 });
+

m-tree/mtree.js

@@ -3,12 +3,12 @@ const { Node, LeafNode, InternalNode, RoutingEntry, GroundEntry } = require('./n
 class MTree {
   /**
    * Constructs a new MTree instance.
-   * @param {number} dimensions - The number of dimensions for data points.
+   * @param {number} dimension - The number of dimension for data points.
    * @param {number} capacity - The maximum number of entries a node can hold before splitting.
    * @param {function} [distanceFunction] - A function to calculate the distance between two points. Defaults to Euclidean distance.
    */
-  constructor(dimensions, capacity, distanceFunction = (a, b) => Math.sqrt(a.map((x, i) => (x - b[i]) ** 2).reduce((sum, x) => sum + x))) {
+  constructor(dimension, capacity, distanceFunction = (a, b) => Math.sqrt(a.map((x, i) => (x - b[i]) ** 2).reduce((sum, x) => sum + x))) {
-    this.dimensions = dimensions;
+    this.dimension = dimension;
     this.capacity = capacity;
     this.distanceFunction = distanceFunction;
     this.root = new LeafNode([], null);
@@ -30,6 +30,16 @@ class MTree {
     if (node.entries.length > this.capacity) {
       this.splitNode(node);
     }
+
+    // Update radius for each routing entry from leaf to root
+    let currentNode = node;
+    while (currentNode.parent) {
+      const routingEntry = currentNode.parent.entries.find(entry => entry.node === currentNode);
+      if (routingEntry) {
+        routingEntry.updateRadius();
+      }
+      currentNode = currentNode.parent;
+    }
   }
 
   /**
@@ -85,84 +95,124 @@ class MTree {
     if (!node) {
       throw new Error('Node is undefined');
     }
+
     const entries = node.entries;
-    const mid = Math.ceil(entries.length / 2);
+    const halfSize = Math.floor(entries.length / 2);
-    const leftEntries = entries.slice(0, mid);
+
-    const rightEntries = entries.slice(mid);
+    let minRadius = Infinity;
-    const leftNode = new LeafNode(leftEntries);
+    let bestSplit = null;
-    const rightNode = new LeafNode(rightEntries);
+
+    // Loop through all combinations of entries that contain half of the total entries
+    const combinations = this.getCombinations(entries, halfSize);
+    // console.log(combinations.map(combination => combination.map(entry => entry.point)), "size: " + combinations.length);
+    for (const combination of combinations) {
+      const leftEntries = combination;
+      const rightEntries = entries.filter(entry => !leftEntries.includes(entry));
+
+      // Calculate the radius for each group
+      const leftRadius = this.calculateRadius(leftEntries);
+      const rightRadius = this.calculateRadius(rightEntries);
+
+      // Calculate the total radius for this split
+      const totalRadius = Math.max(leftRadius, rightRadius);
+
+      // Update the best split if this one has a smaller radius
+      if (totalRadius < minRadius) {
+        minRadius = totalRadius;
+        bestSplit = { leftEntries, rightEntries };
+      }
+    }
+
+    const leftNode = new Node(bestSplit.leftEntries, node.isLeaf);
+    const rightNode = new Node(bestSplit.rightEntries, node.isLeaf);
     leftNode.parent = node; // Set parent of leftNode
     rightNode.parent = node; // Set parent of rightNode
 
-    const leftCentroid = this.calculateCentroid(leftEntries);
+    const rightEntry = new RoutingEntry(rightNode, this);
-    const rightCentroid = this.calculateCentroid(rightEntries);
+    const leftEntry = new RoutingEntry(leftNode, this);
-    const leftRadius = this.calculateRadius(leftEntries, leftCentroid);
-    const rightRadius = this.calculateRadius(rightEntries, rightCentroid);
-    const leftEntry = new RoutingEntry(leftCentroid, leftNode, leftRadius);
-    const rightEntry = new RoutingEntry(rightCentroid, rightNode, rightRadius);
     node.entries = [leftEntry, rightEntry];
     node.isLeaf = false;
   }
 
   /**
-   * Splits the given node into two nodes when the number of entries exceeds capacity.
+   * Calculates the radius of the given entries.
-   * The given node will be left with half of the entries, and a new node is created with the other half.
+   * The radius is the maximum distance from the centroid of the entries to any point in the entries.
-   * The new node is linked to the original node's parent as a sibling by calculating and using the centroid 
-   * as the connecting entry point.
    * 
-   * @param {Node} node - The node to be split.
+   * @param {Object[]} entries - The entries to calculate the radius from.
+   * @returns {number} The radius.
    */
+  calculateRadius(entries) {
+    // Calculate the centroid of the entries
+    const sum = entries.reduce((acc, entry) => {
+      return acc.map((val, i) => val + entry.point[i]);
+    }, new Array(entries[0].point.length).fill(0));
+    const centroidPoint = sum.map(val => val / entries.length);
+
+    // Calculate the maximum distance from the centroid to any point in the entries
+    const maxDistance = Math.max(...entries.map(entry => this.distanceFunction(entry.point, centroidPoint)));
+
+    return maxDistance;
+  }
+
   splitNode(node) {
-    if (!node) {
-      throw new Error('Node is undefined');
-    }
     const entries = node.entries;
-    const mid = Math.ceil(entries.length / 2);
+    const halfSize = Math.floor(entries.length / 2);
-    const leftEntries = entries.slice(0, mid);
+
-    const rightEntries = entries.slice(mid);
+    let minRadius = Infinity;
-    const newNode = new Node(rightEntries, node.isLeaf, node.parent);
+    let bestSplit = null;
+
+    // Loop through all combinations of entries that contain half of the total entries
+    const combinations = this.getCombinations(entries, halfSize);
+    // console.log(combinations.map(combination => combination.map(entry => entry.point)), "size: " + combinations.length);
+    for (const combination of combinations) {
+      const leftEntries = combination;
+      const rightEntries = entries.filter(entry => !leftEntries.includes(entry));
+
+      // Calculate the radius for each group
+      const leftRadius = this.calculateRadius(leftEntries);
+      const rightRadius = this.calculateRadius(rightEntries);
+
+      // Calculate the total radius for this split
+      const totalRadius = Math.max(leftRadius, rightRadius);
+
+      // Update the best split if this one has a smaller radius
+      if (totalRadius < minRadius) {
+        minRadius = totalRadius;
+        bestSplit = { leftEntries, rightEntries };
+      }
+    }
+
+    const newNode = new Node(bestSplit.rightEntries, node.isLeaf, node.parent);
 
     if (node.parent) {
-      const rightCentroid = this.calculateCentroid(rightEntries);
+      // If the node is not a root node, split it into two nodes
-      const rightRadius = this.calculateRadius(rightEntries, rightCentroid);
+      // and link the new node to the original node's parent as a sibling
-      const rightEntry = new RoutingEntry(rightCentroid, newNode, rightRadius);
+      const rightEntry = new RoutingEntry(newNode, this);
       node.parent.entries.push(rightEntry);
 
       if (node.parent.entries.length > this.capacity)
+        // If the parent node now has more than capacity entries, split it too
         this.splitNode(node.parent);
 
-      node.entries = leftEntries;
+      node.entries = bestSplit.leftEntries;
     } else {
+      // If the node is a root node, split it into two new nodes
       this.splitRoot(node);
     }
   }
 
-  /**
+  // Helper function to generate all combinations of a given size
-   * Calculates the centroid of a given set of entries.
+  getCombinations(arr, size) {
-   * The centroid is the average position of all the points in the entries, calculated dimension-wise.
+    if (size === 0) return [[]];
-   *
+    const combinations = [];
-   * @param {Object[]} entries - An array of entries, each with a 'point' property that is an array of numbers.
+    for (let i = 0; i < arr.length; i++) {
-   * @returns {number[]} The centroid of the entries as an array of numbers representing the average position.
+      const current = arr[i];
-   */
+      const rest = arr.slice(i + 1);
-  calculateCentroid(entries) {
+      for (const combination of this.getCombinations(rest, size - 1)) {
-    const centroid = new Array(this.dimensions).fill(0);
+        combinations.push([current, ...combination]);
-    for (const entry of entries) {
-      for (let i = 0; i < this.dimensions; i++) {
-        centroid[i] += entry.point[i];
       }
     }
-    return centroid.map(x => x / entries.length);
+    return combinations;
-  }
-  
-  /**
-   * Calculates the maximum distance from the given centroid to any of the given entries.
-   *
-   * @param {Object[]} entries - An array of entries, each with a 'point' property that is an array of numbers.
-   * @param {number[]} centroid - The centroid to calculate the distance from.
-   * @returns {number} The maximum distance from the centroid to any of the entries.
-   */
-  calculateRadius(entries, centroid) {
-    return Math.max(...entries.map(entry => this.distanceFunction(entry.point, centroid)));
   }
 
   /**
@@ -172,10 +222,10 @@ class MTree {
    * @returns {number[][]} An array of points that are within the radius of the query point.
    */
   rangeQuery(queryPoint, radius) {
-    console.log(`rangeQuery: queryPoint=${JSON.stringify(queryPoint)}, radius=${radius}`);
+    //console.log(`rangeQuery: queryPoint=${JSON.stringify(queryPoint)}, radius=${radius}`);
     const result = [];
     this.rangeQueryRecursive(this.root, queryPoint, radius, result);
-    console.log(`rangeQuery: result=${JSON.stringify(result)}`);
+    //console.log(`rangeQuery: result=${JSON.stringify(result)}`);
     return result;
   }
 
@@ -188,20 +238,20 @@ class MTree {
    * @returns {undefined}
    */
   rangeQueryRecursive(node, queryPoint, radius, result) {
-    console.log(`rangeQueryRecursive: node=${node.id}, queryPoint=${JSON.stringify(queryPoint)}, radius=${radius}`);
+    //console.log(`rangeQueryRecursive: node=${node.id}, queryPoint=${JSON.stringify(queryPoint)}, radius=${radius}`);
     if (node.isLeaf) {
       for (const entry of node.entries) {
-        console.log(`rangeQueryRecursive: checking ground entry ${entry}`);
+        //console.log(`rangeQueryRecursive: checking ground entry ${entry}`);
         if (entry instanceof GroundEntry && this.distanceFunction(queryPoint, entry.point) <= radius) {
           result.push(entry.point);
         }
       }
     } else {
       for (const entry of node.entries) {
-        console.log(`rangeQueryRecursive: checking routing entry ${entry}`);
+        //console.log(`rangeQueryRecursive: checking routing entry ${entry}`);
         const distance = this.distanceFunction(queryPoint, entry.point);
         if (distance > radius + entry.radius) {
-          console.log(`rangeQueryRecursive: regions do not overlap, stopping the recursion on this branch`);
+          //console.log(`rangeQueryRecursive: regions do not overlap, stopping the recursion on this branch`);
           continue;
         }
         this.rangeQueryRecursive(entry.node, queryPoint, radius, result);

m-tree/nodes.js

@@ -1,14 +1,40 @@
+const MTree = require("./mtree");
+
 class RoutingEntry {
   /**
-   * Create a new routing entry
+   * Creates a new routing entry.
-   * @param {number[]} point - The point of the entry
+   * Initializes the routing entry with the given node and dimension,
+   * and computes the initial centroid and radius for the node's entries.
    * @param {Node} node - The node associated with the entry
-   * @param {number} radius - The radius of the entry
+   * @param {MTree} mtree - The number of dimensions for the entry
    */
-  constructor(point, node, radius = 0) {
+  constructor(node, mtree) {
-    this.point = point;
     this.node = node;
-    this.radius = radius;
+    this.mtree = mtree;
+    this.updateCentroid();
+    this.updateRadius();
+  }
+
+  /**
+   * Updates the centroid of the routing entry.
+   * Computes the average position of all points in the associated node's entries.
+   */
+  updateCentroid() {
+    const centroid = new Array(this.mtree.dimension).fill(0);
+    for (const entry of this.node.entries) {
+      for (let i = 0; i < this.mtree.dimension; i++) {
+        centroid[i] += entry.point[i];
+      }
+    }
+    this.point = centroid.map(x => x / this.node.entries.length);
+  }
+  
+  /**
+   * Updates the radius of the routing entry.
+   * Determines the maximum distance from the centroid to any point in the node's entries.
+   */
+  updateRadius() {
+    this.radius = Math.max(...this.node.entries.map(entry => this.mtree.distanceFunction(entry.point, this.point)));
   }
 }