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Fixstars Amplify is used to solve the 14 NP problems presented in the paper, A. Lucas, Front.
In this tutorial, we will partition a graph into two sets with the same number of vertices so that we
minimize the number of edges connecting two points belonging to different sets.
For a given graph, we find the subset of vertices that has the most significant number of vertices where
an edge connects any two vertices in the subset.
Suppose we have a set and are given several subsets of that set. In the exact cover problem, we choose
subsets so that precisely one of the selected subsets contains any element of the set.
Suppose we have a set and are given several subsets of the set. In the set packing problem, we choose the
subsets that have no common part so that the number of elements in the chosen subset is maximized.
A vertex cover is a subset of the vertices of a graph such that every edge of the graph is connected to a
vertex of this subset. The minimum vertex cover problem finds the vertex cover with the fewest elements.
Given a single Boolean formula, it may be possible to make the value of the formula true by successfully
determining the values of the variables in it. The satisfiability problem determines this, and we will
solve a problem called 3-SAT.
In this tutorial, we will find a subset of the edges of a given graph where the edges in the subset are
not adjacent to each other, and the edges not in the subset are always adjacent to the edges in the
subset, with the fewest elements.
The graph coloring problem involves coloring the vertices of a graph with a given number of colors and
determining whether or not the vertices connected by edges can be colored with different colors.
Given a graph and a certain number of colors, the clique cover problem is the problem of determining
whether it is possible to paint the vertices of the graph so that edges connect all pairs of vertices of
the same color.
Suppose you have several jobs and machines, and you know how long each job will take. You assign each job
to one of the machines. The job scheduling problem asks how to assign the jobs to complete all jobs as
quickly as possible.
For a given graph, a closed path that passes through all graph vertices once and returns to its origin is
called a Hamiltonian cycle, and in general, for large graphs, it is difficult to determine whether such a
Given a directed graph, a directed feedback vertex set is a subset of graph vertices such that the closed
path of any graph passes through at least one vertex in the subset. The directed feedback vertex set
problem seeks to find a set with the fewest elements.
Given a directed graph, a feedback edge set is a subset of graph edges where every closed path contains
at least one edge in this subset. The minimum feedback edge set problem searches for a feedback edge set
with the fewest elements.
Two given graphs are said to be isomorphic if there is a one-to-one correspondence between their vertices
and if the two corresponding vertices are both connected by an edge. It is generally challenging to
determine isomorphism, but this example program tackles this problem.
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