Implementing a lightning fast route search engine in Typescript SFNode April 2018

Symfony since 2015 (PHP framework) Titouan Galopin @tgalopin Created bus.io in 2015 (public transport app : https://getbus.io)

Agenda 1. Goal 2. The routing problem 3. Historic solutions 4. Connection Scan Algorithm 5. Implementation

Goal

Let users find the quickest way to go from a point A (coordinates) to point B by bus

“I want to go from the Golden Gate Bridge to LinkedIn Headquarters leaving at 6:58”

The routing problem

This problem is not new, mathematicians already thought about it

This problem is not new, mathematicians already thought about it Fortunately, in Computer Science we love Mathematics!

Equivalent problem in Maths: Shortest Path Problem (SPP)

Graphs

Graphs Invented in 1735 by Euler

Graphs Invented in 1735 by Euler Powerful model for Computer Science (from AI to blockchain, compilers, ...)

Non-oriented Oriented Source : https://fr.wikipedia.org/wiki/Théorie_des_graphes

Source : https://en.wikipedia.org/wiki/Shortest_path_problem SPP : weighted oriented graphs

Historic solutions

Djikstra algorithm: 1956 O(n * log n) n: number of nodes m : number of edges

Djikstra algorithm: 1956 O(n * log n) Bellman–Ford algorithm: 1958 O(n * m) n: number of nodes m : number of edges

Djikstra algorithm: 1956 O(n * log n) Bellman–Ford algorithm: 1958 O(n * m) A* algorithm: 1968 Extension of Djikstra, O(n * log n) but much better in real life, most used today n: number of nodes m : number of edges

Still today, the best generic algorithm to solve SPP is in O(n * log n) n: number of nodes m : number of edges

What about more specific problems like public transports?

Main difference : the bus/train/… has specific timetables => additional constraint => better complexity?

Connection Scan Algorithm

Connection Scan Algorithm Developed in Germany in 2012

Connection Scan Algorithm Developed in Germany in 2012 Targets SPP with timetables

Connection Scan Algorithm Developed in Germany in 2012 Targets SPP with timetables Overall complexity: O(c * log c) Runtime complexity: O(c) Linear!

Connection A to B 7:42 to 7:45

A to B 7:00 to 7:05 B to C 7:06 to 7:09 B to D 7:07 to 7:11 C to E 7:10 to 7:15 B to E 7:11 to 7:18 G to D 7:08 to 7:11 D to E 7:12 to 7:17 E to F 7:20 to 7:29 List of connections instead of Graph ... ...

Implementation

Preparation (before the query) Create a list of all the connections ordered by ascending departing time O(c * log c)

Runtime (during the query)

// Map of the the fastest ways to go to each stop // node name => fastest connection to go to the node let inConnection: StringMap = {}; // Map of earliest arrival time per node // node name => arrival time // (418 = 6 * 60 + 58) let arrivalTimes: StringMap = { A: 418 };

for (let i in connections) { const connection = connections[i]; // If we never arrived to this connection’s departure stop, // we never will as connections are ordered by departure time if (typeof arrivalTimes[connection.departure_stop] === 'undefined') { continue; } // If the connection leaves before we arrive at its departure, it can't be used if (arrivalTimes[connection.departure_stop] > connection.departure_time) { continue; } // If there already was a connection but the previous connection arrived // earlier, keep the previous one if (arrivalTimes[connection.arrival_stop] < connection.arrival_time) { continue; } // Otherwise, we know for sure this connection is better than what we had arrivalTimes[connection.arrival_stop] = connection.arrival_time; inConnection[connection.arrival_stop] = connection; } A to B 7:00 to 7:05 B to C 7:06 to 7:09 B to D 7:07 to 7:11 C to E 7:10 to 7:15 B to E 7:11 to 7:18 G to D 7:08 to 7:11 D to E 7:12 to 7:17

for (let i in connections) { const connection = connections[i]; // If we never arrived to this connection’s departure stop, // we never will as connections are ordered by departure time if (typeof arrivalTimes[connection.departure_stop] === 'undefined') { continue; } // If the connection leaves before we arrive at its departure, it can't be used if (arrivalTimes[connection.departure_stop] > connection.departure_time) { continue; } // If there already was a connection but the previous connection arrived // earlier, keep the previous one if (arrivalTimes[connection.arrival_stop] < connection.arrival_time) { continue; } // Otherwise, we know for sure this connection is better than what we had arrivalTimes[connection.arrival_stop] = connection.arrival_time; inConnection[connection.arrival_stop] = connection; } A to B 7:00 to 7:05 B to C 7:06 to 7:09 B to D 7:07 to 7:11 C to E 7:10 to 7:15 B to E 7:11 to 7:18 G to D 7:08 to 7:11 D to E 7:12 to 7:17

for (let i in connections) { const connection = connections[i]; // If we never arrived to this connection’s departure stop, // we never will as connections are ordered by departure time if (typeof arrivalTimes[connection.departure_stop] === 'undefined') { continue; } // If the connection leaves before we arrive at its departure, it can't be used if (arrivalTimes[connection.departure_stop] > connection.departure_time) { continue; } // If there already was a connection but the previous connection arrived // earlier, keep the previous one if (arrivalTimes[connection.arrival_stop] < connection.arrival_time) { continue; } // Otherwise, we know for sure this connection is better than what we had arrivalTimes[connection.arrival_stop] = connection.arrival_time; inConnection[connection.arrival_stop] = connection; } A to B 7:00 to 7:05 B to C 7:06 to 7:09 B to D 7:07 to 7:11 C to E 7:10 to 7:15 B to E 7:11 to 7:18 G to D 7:08 to 7:11 D to E 7:12 to 7:17

for (let i in connections) { const connection = connections[i]; // If we never arrived to this connection’s departure stop, // we never will as connections are ordered by departure time if (typeof arrivalTimes[connection.departure_stop] === 'undefined') { continue; } // If the connection leaves before we arrive at its departure, it can't be used if (arrivalTimes[connection.departure_stop] > connection.departure_time) { continue; } // If there already was a connection but the previous connection arrived // earlier, keep the previous one if (arrivalTimes[connection.arrival_stop] < connection.arrival_time) { continue; } // Otherwise, we know for sure this connection is better than what we had arrivalTimes[connection.arrival_stop] = connection.arrival_time; inConnection[connection.arrival_stop] = connection; } A to B 7:00 to 7:05 B to C 7:06 to 7:09 B to D 7:07 to 7:11 C to E 7:10 to 7:15 B to E 7:11 to 7:18 G to D 7:08 to 7:11 D to E 7:12 to 7:17

for (let i in connections) { const connection = connections[i]; // If we never arrived to this connection’s departure stop, // we never will as connections are ordered by departure time if (typeof arrivalTimes[connection.departure_stop] === 'undefined') { continue; } // If the connection leaves before we arrive at its departure, it can't be used if (arrivalTimes[connection.departure_stop] > connection.departure_time) { continue; } // If there already was a connection but the previous connection arrived // earlier, keep the previous one if (arrivalTimes[connection.arrival_stop] < connection.arrival_time) { continue; } // Otherwise, we know for sure this connection is better than what we had arrivalTimes[connection.arrival_stop] = connection.arrival_time; inConnection[connection.arrival_stop] = connection; } A to B 7:00 to 7:05 B to C 7:06 to 7:09 B to D 7:07 to 7:11 C to E 7:10 to 7:15 B to E 7:11 to 7:18 G to D 7:08 to 7:11 D to E 7:12 to 7:17

A to B 7:00 to 7:05 B to C 7:06 to 7:09 B to D 7:07 to 7:11 C to E 7:10 to 7:15 B to E 7:11 to 7:18 G to D 7:08 to 7:11 D to E 7:12 to 7:17 // We know these times are // the earliest possible arrival // times for each stop arrivalTimes: A: 6:58 B: 7:05 C: 7:09 D: 7:11 E: 7:15 // Moreover, we get a list of the // fastest way to get to each node inConnection: B: C: D: E: A to B 7:00 to 7:05 B to C 7:06 to 7:09 B to D 7:07 to 7:11 C to E 7:10 to 7:15

inConnection: B: C: D: E: A to B 7:00 to 7:05 B to C 7:06 to 7:09 B to D 7:07 to 7:11 C to E 7:10 to 7:15 let steps = []; let current = 'E'; while (current !== 'A') { let step = inConnection[current]; current = step['departure_stop']; steps.push(step); } // Result: A -> B -> C -> E

More features! Handle walks between stops and at the start/end of the journey Select the 5 best results in the next minutes

But how to keep performance? Async!

OSRM for walks Modern C++ routing engine for shortest paths in road networks http://project-osrm.org

Search leaving at time T Prepare in advance the connections Load the connections CSA Result 1 Query Search leaving at time T + 1 Search leaving at time T + 2 ... Select best results User Prepare in advance the walks between stops Find walks from start point Find walks to end point CSA Result 2 Search leaving at time T + 3

In production https://getbus.io 370 nodes 10998 connections 20 results computed, 10 bests selected 150ms per query

Thanks! Questions?