Optimal Transportation Networks

Models and Theory

  • Marc Bernot
  • Vicent Caselles
  • Jean-Michel Morel

Part of the Lecture Notes in Mathematics book series (LNM, volume 1955)

About this book


The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees.
These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.


Approximation Irrigation Monge-Kantorovich problem Optimal transport Traffic plans Transportation networks

Authors and affiliations

  • Marc Bernot
    • 1
  • Vicent Caselles
    • 2
  • Jean-Michel Morel
    • 3
  1. 1.Unité de mathématiques pures et appliquéesENS LyonLyon Cedex 7France
  2. 2.Dept. de Tecnologies de la Informació i les ComunicacionsPompeu Fabra UniversityBarcelonaSpain
  3. 3.CMLAEcole Normale Supérieure de CachanCachan CedexFrance

Bibliographic information