Covering problems in edge- and node-weighted graphs

Covering Problems in Edge- and Node-Weighted Graphs

This paper discusses the graph covering problem in which a set of edges in an edgeand nodeweighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large integrality gap of a natural linear programming (LP) relaxation, LP rounding algorithms based on the relaxation yield poor performance. Here we propose a stronger LP ...

Watersheds, waterfalls, on edge or node weighted graphs

Fernand MeyerCentre de Morphologie MathématiqueMines-ParisTech () Watersheds, waterfalls, on edge or node weighted graphs 2012 February 29 1 / 201 arXi Introduction The watershed transform is one of the major image segmentation tools [4], used in the community of mathematical morphology and beyond. If the watershed is a successful concept, there is another side of the coin: a number of definiti...

Watersheds on edge or node weighted graphs "par l'exemple"

Watersheds have been defined both for node and edge weighted graphs. We show that they are identical: for each edge (resp. node) weighted graph exists a node (resp. edge) weighted graph with the same minima and catchment basin.

Edge covering of acyclic graphs

Edge searching weighted graphs

In traditional edge searching one tries to clean all of the edges in a graph employing the least number of searchers. It is assumed that each edge of the graph initially has a weight equal to one. In this paper we modify the problem and introduce the Weighted Edge Searching Problem by considering graphswith arbitrary positive integerweights assigned to its edges. We give bounds on the weighted ...