The shortest way to visit all metro lines in Paris

by   Florian Sikora, et al.
Université Paris-Dauphine

What if {a tourist, a train addict, Dr. Sheldon Cooper, somebody who likes to waste time} wants to visit all metro lines or carriages in a given network in a minimum number of steps? We study this problem with an application to the Parisian metro network and propose optimal solutions thanks to mathematical programming tools. Quite surprisingly, it appears that you can visit all 16 Parisian metro lines in only 26 steps (we denote by a step the act of taking the metro from one station to an adjacent one). Perhaps even more surprisingly, adding the 5 RER lines to these 16 lines does not increase the size of the best solution.


page 4

page 6

page 9

page 11

page 12

page 14

page 16


Catching a Polygonal Fish with a Minimum Net

Given a polygon P in the plane that can be translated, rotated and enlar...

Halving by a Thousand Cuts or Punctures

For point sets P_1, …, P_, a set of lines L is halving if any face of t...

Doubly transitive lines II: Almost simple symmetries

We study lines through the origin of finite-dimensional complex vector s...

Stabbing Convex Bodies with Lines and Flats

We study the problem of constructing weak -nets where the stabbing eleme...

Doubly transitive lines I: Higman pairs and roux

We study lines through the origin of finite-dimensional complex vector s...

A rigorous definition of axial lines: ridges on isovist fields

We suggest that 'axial lines' defined by (Hillier and Hanson, 1984) as l...

Studying Topology of Time Lines Graph leads to an alternative approach to the Newcomb's Paradox

The Newcomb's paradox is one of the most known paradox in Game Theory ab...

Please sign up or login with your details

Forgot password? Click here to reset