What is edge in edge coverage?
An edge cover is a subset of edges defined similarly to the vertex cover (Skiena 1990, p. 219), namely a collection of graph edges such that the union of edge endpoints corresponds to the entire vertex set of the graph. Therefore, only graphs with no isolated points have an edge cover.
What is the vertex cover problem?
The vertex cover problem is an NP-Complete problem, which means that there is no known polynomial-time solution for finding the minimum vertex cover of a graph unless it can be proven that P = NP. There, however, exists polynomial-time approximate algorithms to find the vertex cover of a graph.
What is graph covering problem?
1.1 Definition. Graph covering includes a wide range of problems which are closely related with graph partitioning and graph colouring problems. The two main types of graph covering problems are graph covering by another graph and vertex covering problems. 1.1.1 Graph Covering by Another Graph.
Is edge cover NP complete?
Computing total edge covers. We now consider the t-Total Edge Cover problem. For this problem becomes the Edge Cover problem, which has long been known to be solvable in polynomial time [8]. The problem is NP-complete for each fixed 2 ≤ t ≤ k [9, Theorem 3].
What is edge coverage in testing?
Edge coverage reports which branches or code decision points were executed to complete the test. They both report a coverage metric, measured as a percentage. The meaning of this depends on what form(s) of coverage have been used, as 67% branch coverage is more comprehensive than 67% statement coverage.
What is node coverage and edge coverage?
▶ Node coverage corresponds to statement coverage, edge coverage corresponds to something like branch coverage. Covering all execution paths is impossible with loops, so there are various approximations. Don’t forget the distinction between syntactic and semantic reachability.
What is a vertex cover problem discuss Graham’s algorithm in detail?
A Vertex Cover of a graph G is a set of vertices such that each edge in G is incident to at least one of these vertices. The decision vertex-cover problem was proven NPC. Now, we want to solve the optimal version of the vertex cover problem, i.e., we want to find a minimum size vertex cover of a given graph.
What is the size of the vertex cover?
The size of the minimum vertex cover is 1 (by taking either of the endpoints). 3. Star: |V | − 1 vertices, each of degree 1, connected to a central node. The size of the minimum vertex cover is k − 1 (by taking any less vertices we would miss an edge between the remaining vertices).
What is edge cover in graph theory?
In graph theory, an edge cover of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set. In computer science, the minimum edge cover problem is the problem of finding an edge cover of minimum size.
Is vertex cover an NPC?
Thus, vertex cover is NP Hard. Since vertex cover is in both NP and NP Hard classes, it is NP Complete.
What is node coverage and EDGE coverage?
What is an edge cover problem?
It is an optimization problem that belongs to the class of covering problems and can be solved in polynomial time . Formally, an edge cover of a graph G is a set of edges C such that each vertex in G is incident with at least one edge in C.
What are the advantages of edge covering?
An edge cover might be a good way to solve a problem if the answer needs to include all nodes of a graph. Many times, themes from edge covering are adapted and integrated into other problems.
What is covering problem?
Covering problems are minimization problems and usually linear programs, whose dual problems are called packing problems. The most prominent examples of covering problems are the set cover problem, which is equivalent to the hitting set problem, and its special cases, the vertex cover problem and the edge cover problem.
What is the edge covering number?
The edge covering number is the size of a minimum edge covering. The following figure shows examples of minimum edge coverings. Note that the figure on the right is not only an edge cover but also a matching. In particular, it is a perfect matching: a matching M in which each vertex is incident with exactly one edge in M.