## Introduction

I wrote a blog post in French that had some unexpected success (by success I mean that people actually read it). At least two people asked for an English translation. So here it goes, with some of the errors in the French version corrected.

Formally we would speak of “shortest path in a graph problem”. The goal is the same: what is the shortest way to go from A to B.

Route computation are nice as the actual use cases can be explained to anyone:

- the GPS end user
- the computer science student that at some point learnt the basic algorithms
- there is still research going on, but it can be explained to anyone interested within a few pints

Personally, what I find interesting is how those algorithms evolved through time. Sorry for punctual technical details.

## 1956 – 1958: Ford, Moore and Bellman

The first suggested algorithm was published independently by those authors.

It is nowadays usually called the *Bellman-Ford* algorithm.

## 1959: Dijkstra

Edgard Dijkstra is Dutch.

He is one of the big names in computer science. He is know for his handwriting and quotes such as:

`Simplicity is prerequisite for reliability``The question of whether Machines Can Think... is about as relevant as the question of whether Submarines Can Swim``Object-oriented programming is an exceptionally bad idea which could only have originated in California`

He is the author of — brace yourself — *Dijkstra’s algorithm* published in 1959.
It has been described in a two pages only article but the name stuck
as the fundamental brick of route computations.

However, the algorithm we learn at school is not the one published by Dijkstra. It has a complexity of O(n²) while we are teached that complexity of the algorithm is O(n·log(n)).

We had to wait 28 year to get to it.

## 1987: Tarjan

The weakness of Dijkstra’s algorithm is its priority queue that returns what node to visit next. An article from 1987 by Tarjan (an other reference in the world of graphs) brings us to the “modern” Dijkstra’s algorithm.

Many variations have been tested to speed up the algorithm with mitigated success, such as A*, bi-directional searches, sacrificing the optimality or a combination of all that.

On a recent computer, computing a route across France takes around a second. Therefor back in the 90’s it was way to slow. There was a need to speed up the computation.

We had to wait 18 year to get to it.

## 2005: Dimacs challenge and rise of the KIT

The 9th Dimac Challenge was about routes computation. For this event the road network of the United States was published.

A large number of publications pulverised all the records. The algorithms are now fast enough to compute a route between two points on earth in less
than a millisecond (more than a *thousands* times faster than the Dijkstra’s algorithm).

An overwhelming share of publications come from from the Karlsruhe Institute of Technology.

The team members suggested many algorithms, but also tested nearly every possible combination between those algorithms.

There were so many publications it was hard to know where to look.

## 2008: consolidation with the Contraction Hierarchies

After this phase of exuberant creativity, we could extract the core substance to make the algorithm that will probably become the new reference:
the *contraction hierarchies*.

It has been presented in a master thesis (so I am somewhat ashamed of my PhD thesis…) by Geisberger.

There is nothing really new, only the removal of superfluous ideas that made other algorithms too complicated to keep the smallest core that works well.

Everybody that is interested in algorithmic should read the algorithm and its demonstration of optimality. The first time I read it, I could not grasp how it worked. I had to walk through the demonstration to be convinced.

That algorithm is used in OSRM, a free route calculator based on OpenStreetMap data.

## 2009: public transit are still forgotten

At last we know to efficiently compute a route on a street network. What about public transit? Not so bright here.

The question was already studied in 1991 in the great PhD thesis of Eduard Tulp. But little happened since.

Performances are deceiving and trying to use the successes in street network failed.

In the article Car or Public Transport—Two Worlds H. Bast show the differences that exist between both means of transportation and that is not interesting to try to use the same techniques.

## 2010: transfer patterns, performance, at last!

It was summer, I had just sent my thesis manuscript to the examiners. Because of over-zealousness I read the latest article from H. Bast.

For the first time it was possible to compute routes using public transit within a few milliseconds in a large city as New-York.

If you looked closely, the was still a slight twist: the authors used the computing power of thousands of computers from Google. A massive pre-processing is the key to such good results.

Just two more years to wait to have an effective algorithm.

## 2012: Delling’s Raptor

Daniel Delling likes cool names (a previous algorithm was called *Sharc*). He chose Raptor for his new algorithm.

The proposed approach has no need for pre-processing and has better performances than the transfer patterns.

Hooray! Cars do not have any more the monopole on efficient algorithm. Raptor has the advantage to be rather simple and to have nice properties (too technical to bother you with them).

## Intermission: opendata and science

Science needs data to be easily available. The DIMACS challenge was a success because big real life data set were published.

It took six years from the first high-performance street network routing algorithm to the first high performance algorithm on public transit. We had to wait so long until data sets were at last released.

It is the opendata movement applied to transportation that allowed that scientific progress.

## 2013: Connection Scan Algorithm

A last one! In an article very modestly called Intriguingly Simple and Fast Transit Routing
the authors present the *connection scan algorithm*. It is slightly more efficient than Raptor but is considerably more simple.

When reading the article, and once again when implementing it, I was struck how braindead simple it is, but it works.

We went through 57 years of research to end up with an algorithm that could have been written at the same time as Dijkstra’s.

Hence a last quote of Dijkstra that seems very appropriate:

`Simplicity is a great virtue but it requires hard work to achieve it and education to appreciate it. And to make matters worse: complexity sells better`