This paper defines floodings on edge weighted and on node weighted graphs. Of particular interest are the highest floodings of a graph below a ceiling function defined on the nodes. It is shown that each flooding on a node weighted graph may be interpreted as a flooding on an edge weighted graphs with appropriate weights on the edges. The highest flooding of a graph under a ceiling function is then interpreted as a shortest distance on an augmented graph, using the ultrametric distance function. Thanks to this remark, the classical shortest distance algorithms may be used for constructing floodings.


Neighboring Node Edge Weight Weighted Graph Outgoing Edge Node Weight 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Fernand Meyer
    • 1
  1. 1.CMM-Centre de Morphologie Mathématique, Mathématiques et SystèmesMINES ParisTechFrance

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