Flooding Edge or Node Weighted Graphs
Résumé
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.