Improve navigation graph compression

script/output-graph.js

@@ -1,23 +1,43 @@
 #!/usr/bin/env -S node --experimental-json-modules
 
 import network from "../src/tam/network.json";
+import color from "color";
 
 console.log("digraph {");
-console.log("graph[layout=neato, overlap=scalexy, splines=true, outputorder=nodesfirst]");
+console.log(`graph[\
+    layout=neato, \
+    mode=ipsep, \
+    overlap=ipsep, \
+    outputorder=nodesfirst, \
+]`);
 
-for (const [stopId, stop] of Object.entries(network.stops)) {
+const stops = new Set();
-    console.log(`${stopId}[label="${stop.properties.name}", shape=box]`);
+
+for (const stop of Object.values(network.stops)) {
+    stops.add(stop.properties.node);
+
+    const {node, name, routes} = stop.properties;
+    const backgrounds = routes.map(([line]) => network.lines[line].color);
+    const font = color(backgrounds[0]).isLight() ? "black" : "white";
+
+    console.log(`${node}[\
+        label="${name}", \
+        style=striped, \
+        fillcolor="${[...new Set(backgrounds)].join(":")}", \
+        fontcolor="${font}", \
+        shape=box, \
+    ]`);
 }
 
 const junctions = new Set();
 
 for (const [beginId, begin] of Object.entries(network.navigation)) {
-    if (!(beginId in network.stops)) {
+    if (!stops.has(beginId)) {
         junctions.add(beginId);
     }
 
     for (const endId in begin) {
-        if (!(endId in network.stops)) {
+        if (!stops.has(endId)) {
             junctions.add(endId);
         }
     }
@@ -29,7 +49,7 @@ for (const junction of junctions) {
 
 for (const [beginId, begin] of Object.entries(network.navigation)) {
     for (const endId in begin) {
-        console.log(`${beginId} -> ${endId}`);
+        console.log(`${beginId} -> ${endId}[len=2]`);
     }
 }
 

src/tam/network.js

@@ -70,7 +70,7 @@ import * as osm from "./sources/osm.js";
  */
 
 /**
- * Edge of the graph for out-of-route navigation between stops.
+ * Edge of the graph for navigating between stops.
  * @typedef {Object} NavigationEdge
  * @property {string} type Always equal to "Feature".
  * @property {Object} properties
@@ -83,13 +83,18 @@ import * as osm from "./sources/osm.js";
  * Sequence of points forming this edge (as longitude/latitude pairs).
  */
 
+/**
+ * Graph for navigating between stops.
+ * @typedef {Object.<string,Object.<string,NavigationEdge>>} Navigation
+ */
+
 /**
  * Information about a public transport network.
  * @typedef {Object} Network
  * @property {Object.<string,Stop>} stops List of stops.
  * @property {Object.<string,Line>} lines List of lines.
  * @property {Object.<string,Segment>} segments List of segments.
- * @property {Object.<string,Object.<string,NavigationEdge>>} navigation
+ * @property {Navigation} navigation
  * Graph for out-of-route navigation between stops.
  */
 
@@ -332,45 +337,20 @@ different sequence of nodes in two or more lines.`);
 };
 
 /**
- * Create a graph for navigating between stops outside of
+ * Create a graph for navigating between stops.
- * regular planned routes.
- * @property {Object.<string,Stop>} stops List of stops.
  * @param {Array.<Object>} elementsList List of nodes retrieved from OSM.
  * @param {Object.<string,Object>} elementsById OSM nodes indexed by their ID.
  * @return {Object.<string,Object.<string,NavigationEdge>} Resulting graph.
  */
-const createNavigationGraph = (stops, elementsList, elementsById) => {
+const createNavigationGraph = (elementsList, elementsById) => {
-    // Graph of network stops and junctions
     const navigation = {};
-
-    // Predecessors of each graph node
     const navigationReverse = {};
 
-    // Stops indexed by their OSM ID instead of their network ID
-    const stopsReverse = Object.fromEntries(
-        Object.entries(stops).map(([id, stop]) => [stop.properties.node, id])
-    );
-
-    // Get the ID of a node in the navigation graph
-    // (its network ID if it is a network object, otherwise its OSM id)
-    const getNavigationId = objId => (
-        objId in stopsReverse
-        ? stopsReverse[objId]
-        : objId.toString()
-    );
-
-    // Get the OSM ID of a navigation object
-    const getOSMId = navId => (
-        navId in stops
-        ? stops[navId].properties.node
-        : navId
-    );
-
     // Create graph nodes from OSM nodes
     for (const obj of elementsList) {
         if (obj.type === "node") {
-            navigation[getNavigationId(obj.id)] = {};
+            navigation[obj.id] = {};
-            navigationReverse[getNavigationId(obj.id)] = {};
+            navigationReverse[obj.id] = {};
         }
     }
 
@@ -378,95 +358,202 @@ const createNavigationGraph = (stops, elementsList, elementsById) => {
     for (const obj of elementsList) {
         if (obj.type === "way") {
             const oneWay = osm.isOneWay(obj);
-            const pairs = obj.nodes.slice(0, -1).map(
-                (node, i) => [
-                    getNavigationId(node),
-                    getNavigationId(obj.nodes[i + 1]),
-                ]
-            );
 
-            for (const [from, to] of pairs) {
+            for (let i = 0; i + 1 < obj.nodes.length; ++i) {
-                navigation[from][to] = [from, to];
+                const from = obj.nodes[i];
+                let to = obj.nodes[i + 1];
+                let path = [from.toString(), to.toString()];
+
+                // Make sure we can’t jump between rails at railway crossings
+                if (i + 2 < obj.nodes.length
+                        && osm.isRailwayCrossing(elementsById[to])) {
+                    const next = obj.nodes[i + 2];
+                    path = [from.toString(), to.toString(), next.toString()];
+                    to = next;
+                    i += 1;
+                }
+
+                navigation[from][to] = path;
                 navigationReverse[to][from] = true;
 
                 if (!oneWay) {
-                    navigation[to][from] = [to, from];
+                    const reversePath = [...path];
+                    reversePath.reverse();
+                    navigation[to][from] = reversePath;
                     navigationReverse[from][to] = true;
                 }
             }
         }
     }
 
-    // Mark nodes of the graph to be kept
+    return { navigation, navigationReverse };
-    const nodesToKeep = {};
+};
 
-    for (const nodeId in navigation) {
+/**
-        if (nodeId in stops) {
+ * Remove and relink nodes that connect only two nodes or less.
-            // Keep stop nodes
+ * @param {Object.<string,Stop>} stops List of stops.
-            nodesToKeep[nodeId] = true;
+ * @param {Navigation} navigation Input navigation graph.
-            continue;
+ * @param {Object.<string,Object.<string,boolean>>} navigationReverse
-        }
+ * Backward edges of the navigation graph.
+ */
+const compressNavigationGraph = (stops, navigation, navigationReverse) => {
+    const stopsReverse = Object.fromEntries(
+        Object.entries(stops).map(([id, stop]) => [stop.properties.node, id])
+    );
 
-        const entries = new Set(Object.keys(navigationReverse[nodeId]));
+    let removedDeadEnds = true;
-        const exits = new Set(Object.keys(navigation[nodeId]));
+    const nodesToCompress = {};
 
-        // Keep split nodes, i.e. nodes with at least two exit nodes
+    while (removedDeadEnds) {
-        // and one entry node that are all distinct from each other
+        // Identify nodes to be compressed
-        if (entries.size >= 1) {
+        for (const nodeId in navigation) {
-            if (exits.size >= 3) {
+            if (nodeId in stopsReverse) {
-                nodesToKeep[nodeId] = true;
+                // Keep stop nodes
                 continue;
             }
 
-            if (exits.size === 2) {
+            const entries = new Set(Object.keys(navigationReverse[nodeId]));
-                for (const entry of entries) {
+            const exits = new Set(Object.keys(navigation[nodeId]));
-                    if (!exits.has(entry)) {
+
-                        nodesToKeep[nodeId] = true;
+            // Keep split nodes, i.e. nodes with at least two exit nodes
-                        continue;
+            // and one entry node that are all distinct from each other
+            if (entries.size >= 1) {
+                if (exits.size >= 3) {
+                    continue;
+                }
+
+                let isSplit = false;
+
+                if (exits.size === 2) {
+                    for (const entry of entries) {
+                        if (!exits.has(entry)) {
+                            isSplit = true;
+                            break;
+                        }
+                    }
+                }
+
+                if (isSplit) {
+                    continue;
+                }
+            }
+
+            // Keep junction nodes, i.e. nodes with at least two entry nodes
+            // and one exit node that are all distinct from each other
+            if (exits.size >= 1) {
+                if (entries.size >= 3) {
+                    continue;
+                }
+
+                let isJunction = false;
+
+                if (entries.size === 2) {
+                    for (const exit of exits) {
+                        if (!entries.has(exit)) {
+                            isJunction = true;
+                            break;
+                        }
+                    }
+                }
+
+                if (isJunction) {
+                    continue;
+                }
+            }
+
+            // Compress all other nodes
+            nodesToCompress[nodeId] = true;
+        }
+
+        // Find nodes that cannot be used to directly link up two kept nodes
+        const usedNodes = {};
+
+        for (const beginId in navigation) {
+            if (beginId in nodesToCompress) {
+                continue;
+            }
+
+            usedNodes[beginId] = true;
+
+            // Start a DFS from each node to be kept
+            const begin = navigation[beginId];
+            const stack = [];
+            const parent = {[beginId]: beginId};
+
+            for (const succId in begin) {
+                if (succId in nodesToCompress) {
+                    stack.push(succId);
+                    parent[succId] = beginId;
+                }
+            }
+
+            while (stack.length > 0) {
+                const endId = stack.pop();
+                const end = navigation[endId];
+
+                if (!(endId in nodesToCompress)) {
+                    let trackback = parent[endId];
+
+                    while (trackback !== beginId) {
+                        usedNodes[trackback] = true;
+                        trackback = parent[trackback];
+                    }
+                } else {
+                    for (const succId in end) {
+                        if (succId !== parent[endId]) {
+                            parent[succId] = endId;
+                            stack.push(succId);
+                        }
                     }
                 }
             }
         }
 
-        // Keep junction nodes, i.e. nodes with at least two entry nodes
+        // Remove dead-end nodes
-        // and one exit node that are all distinct from each other
+        removedDeadEnds = false;
-        if (exits.size >= 1) {
-            if (entries.size >= 3) {
-                nodesToKeep[nodeId] = true;
-                continue;
-            }
 
-            if (entries.size === 2) {
+        for (const beginId in navigation) {
-                for (const exit of exits) {
+            if (!(beginId in usedNodes)) {
-                    if (!entries.has(exit)) {
+                for (const neighborId in navigation[beginId]) {
-                        nodesToKeep[nodeId] = true;
+                    delete navigationReverse[neighborId][beginId];
-                        continue;
-                    }
                 }
+
+                for (const neighborId in navigationReverse[beginId]) {
+                    delete navigation[neighborId][beginId];
+                }
+
+                delete navigation[beginId];
+                delete navigationReverse[beginId];
+                removedDeadEnds = true;
             }
         }
     }
 
-    // Compress edges between nodes of interest
+    // Perform node compression
-    for (const beginId in nodesToKeep) {
+    for (const beginId in navigation) {
+        if (beginId in nodesToCompress) {
+            continue;
+        }
+
+        // Start a DFS from each node to be kept
         const begin = navigation[beginId];
         const stack = [];
         const parent = {[beginId]: beginId};
 
         for (const succId in begin) {
-            stack.push(succId);
+            if (succId in nodesToCompress) {
-            parent[succId] = beginId;
+                stack.push(succId);
+                parent[succId] = beginId;
+            }
         }
 
         while (stack.length > 0) {
             const endId = stack.pop();
             const end = navigation[endId];
 
-            if (endId in nodesToKeep) {
+            if (!(endId in nodesToCompress)) {
-                if (endId in begin) {
+                // Found another kept node
-                    continue;
+                // Collect and remove intermediate nodes
-                }
-
                 const reversePath = [endId];
                 let trackback = parent[endId];
                 let oneWay = !(trackback in end);
@@ -476,6 +563,7 @@ const createNavigationGraph = (stops, elementsList, elementsById) => {
                     oneWay = oneWay || !(parent[trackback] in navigation[trackback]);
 
                     delete navigation[trackback];
+                    delete navigationReverse[trackback];
                     trackback = parent[trackback];
                 }
 
@@ -483,20 +571,24 @@ const createNavigationGraph = (stops, elementsList, elementsById) => {
                 const forwardPath = [...reversePath];
                 forwardPath.reverse();
 
+                // Create edges to link both nodes directly
                 delete begin[forwardPath[1]];
+                delete navigationReverse[endId][reversePath[1]];
+
+                delete end[reversePath[1]];
+                delete navigationReverse[beginId][forwardPath[1]];
 
                 if (!(endId in begin)) {
                     begin[endId] = forwardPath;
+                    navigationReverse[endId][beginId] = true;
                 }
 
-                if (!oneWay) {
+                if (!oneWay && !(beginId in end)) {
-                    delete end[reversePath[1]];
+                    end[beginId] = reversePath;
-
+                    navigationReverse[beginId][endId] = true;
-                    if (!(beginId in end)) {
-                        end[beginId] = reversePath;
-                    }
                 }
             } else {
+                // Continue the traversal down unused nodes
                 let isFirst = true;
 
                 for (const succId in end) {
@@ -511,30 +603,23 @@ non-junction node ${endId}`);
                         }
                     }
                 }
-
-                if (isFirst) {
-                    // Reached a dead-end: remove the path
-                    let trackback = endId;
-
-                    while (parent[trackback] !== beginId) {
-                        delete navigation[trackback];
-                        trackback = parent[trackback];
-                    }
-
-                    delete navigation[trackback];
-                    delete begin[trackback];
-                }
             }
         }
     }
+};
 
-    // Convert graph edges to GeoJSON line strings
+/**
+ * Transform navigation graph edges into GeoJSON segments.
+ * @param {Navigation} navigation Input navigation graph.
+ * @param {Object.<string,Object>} elementsById OSM nodes indexed by their ID.
+ */
+const makeNavigationSegments = (navigation, elementsById) => {
     for (const [beginId, begin] of Object.entries(navigation)) {
         for (const endId in begin) {
             begin[endId] = turfHelpers.lineString(begin[endId].map(
                 nodeId => [
-                    elementsById[getOSMId(nodeId)].lon,
+                    elementsById[nodeId].lon,
-                    elementsById[getOSMId(nodeId)].lat
+                    elementsById[nodeId].lat
                 ]
             ), {
                 begin: beginId,
@@ -544,8 +629,6 @@ non-junction node ${endId}`);
             begin[endId].properties.length = 1000 * turfLength(begin[endId]);
         }
     }
-
-    return navigation;
 };
 
 /**
@@ -561,7 +644,12 @@ export const fetch = async lineRefs => {
     }, {});
 
     const { lines, stops, segments } = processRoutes(elementsList, elementsById);
-    const navigation = createNavigationGraph(stops, elementsList, elementsById);
+    const { navigation, navigationReverse } = createNavigationGraph(
+        elementsList, elementsById
+    );
+
+    compressNavigationGraph(stops, navigation, navigationReverse);
+    makeNavigationSegments(navigation, elementsById);
 
     return { navigation, lines, stops, segments };
 };

src/tam/sources/osm.js

@@ -48,6 +48,19 @@ export const isOneWay = obj => (
         obj.tags.highway === "motorway")
 );
 
+/**
+ * Determine if a node is a railway crossing or not.
+ *
+ * See <https://wiki.osm.org/Tag:railway=railway_crossing> for details.
+ * @param {Object} obj OSM node object.
+ * @return {boolean} Whether the node is a railway crossing.
+ */
+export const isRailwayCrossing = obj => (
+    obj.type === "node" &&
+    isObject(obj.tags) &&
+    (obj.tags.railway === "railway_crossing")
+);
+
 /**
  * Determine if an OSM object is a public transport line (route master).
  *