This technique has given PTASs for the following problems : subgraph isomorphism, maximum independent set, minimum vertex cover, minimum dominating set, minimum edge dominating set, maximum triangle matching, and many others.
42.
Just like the Vertex cover problem is polynomial for tree graphs but NP-hard for general graphs, the square covering problem is linear for hole-free polygons but NP-hard for general polygons.
43.
Result 2 shows that the constraint composite graph can also be used to capture the numerical structure of the weighted constraints ( since a minimum weighted vertex cover can be computed in polynomial time for bipartite graphs ).
44.
In the vertex cover problem, a graph and a natural number are taken as inputs and the algorithm must decide whether there exists a set of vertices such that every edge is incident to a vertex in.
45.
For example, there is an algorithm which solves the vertex cover problem in O ( kn + 1.274 ^ k ) time, where is the number of vertices and is the size of the vertex cover.
46.
For example, there is an algorithm which solves the vertex cover problem in O ( kn + 1.274 ^ k ) time, where is the number of vertices and is the size of the vertex cover.
47.
He proved with his coauthors essentially that a huge class of semidefinite programming algorithms for the famous vertex cover problem will not achieve a solution of value less than the value of the optimal solution times a factor of two.
48.
Put otherwise, we find a maximal matching " M " with a greedy algorithm and construct a vertex cover " C " that consists of all endpoints of the edges in " M ".
49.
The theory of perfect graphs developed from a 1958 result of Tibor Gallai that in modern language can be interpreted as stating that the K�nig's theorem, a much earlier result relating matchings and vertex covers in bipartite graphs.
50.
For graphs that are not bipartite, the maximum matching and minimum vertex cover problems are very different in complexity : maximum matchings can be found in polynomial time for any graph, while minimum vertex cover is NP-complete.
