In this paper, two typical minimum weight covering problems, namely vertex covering problem and edge covering problem, are studied under stochastic environments.
Bhattacharya (2011) applied NSGA-II for solving a vertex covering obnoxious facility location model on a plane was designed with a combination of three objective functions.
All individual datasets (both of patients with ALS and healthy controls) were normalised to the computed group average anatomical surface, allowing for group comparison between patients with ALS and group matched healthy controls at each small sliver of cortical surface (vertex), covering whole brain.
MTO can be translated into a vertex covering problem (see Proposition 1) on a graph class that is K4-free--this motivates to study whether vertex covering on this graph class can be done faster than on general graphs.
We study the approximability of subdense instances of various covering optimization problems, including Vertex Cover, Connected Vertex Cover, Set Cover, and Steiner Tree problems.
Our approximation algorithm makes use of the local ratio technique, which is useful for approximating optimization covering problems such as vertex cover, dominating set, minimum spanning tree, feedback vertex set and more [ 33, 40, 41].
LVGs are strongly connected components with minimal circuit covering vertex set V ~ that consists of one single element v1.
The circuit set C and the minimal circuit covering vertex set V ~ are C = { x 4 }, { x 2, x 3, x 4 }, { x 1, x 2, x 3, x 4 } and V ~ = { x 4 }.
back_track v, vertex_front, route) follows in reverse the route previously taken that found free pebbles at the last vertex_front and it pulls free pebbles through a non-bifurcating chain of vertices back to vertex v while covering the edges as a new directed path.
We focus on the following problem: given an undirected graph with no loop, and a perfect matching on this graph, find a set of cycles and paths covering every vertex of the graph, with edges alternatively in the matching and outside the matching, and satisfying a given constraint on the numbers of cycles and paths.
Then we have the matching (M') of G which obtained from M by replacing the maximum matching of (H _{k_{0}}) by the maximum matching of (hat{H} _{k_{0}}) and by adjusting the maximum matching of each (C_{i}) to the one without covering the vertex (v_{i}), (i=1,ldots, x).
