def METHOD_NAME(self, dag):
    """run the layout method"""
    if not self.coupling_map.is_connected():
        raise TranspilerError(
            "Coupling Map is disjoint, this pass can't be used with a disconnected coupling "
            "map."
        )
    qubits = dag.qubits
    cxs = set()
    from constraint import Problem, AllDifferentConstraint, RecursiveBacktrackingSolver
    from qiskit.transpiler.passes.layout._csp_custom_solver import CustomSolver
    for gate in dag.two_qubit_ops():
        cxs.add((qubits.index(gate.qargs[0]), qubits.index(gate.qargs[1])))
    edges = set(self.coupling_map.get_edges())
    if self.time_limit is None and self.call_limit is None:
        solver = RecursiveBacktrackingSolver()
    else:
        solver = CustomSolver(call_limit=self.call_limit, time_limit=self.time_limit)
    variables = list(range(len(qubits)))
    variable_domains = list(self.coupling_map.physical_qubits)
    random.Random(self.seed).shuffle(variable_domains)
    problem = Problem(solver)
    problem.addVariables(variables, variable_domains)
    problem.addConstraint(AllDifferentConstraint())  # each wire is map to a single qubit
    if self.strict_direction:
        def constraint(control, target):
            return (control, target) in edges
    else:
        def constraint(control, target):
            return (control, target) in edges or (target, control) in edges
    for pair in cxs:
        problem.addConstraint(constraint, [pair[0], pair[1]])
    solution = problem.getSolution()
    if solution is None:
        stop_reason = "nonexistent solution"
        if isinstance(solver, CustomSolver):
            if solver.time_current is not None and solver.time_current >= self.time_limit:
                stop_reason = "time limit reached"
            elif solver.call_current is not None and solver.call_current >= self.call_limit:
                stop_reason = "call limit reached"
    else:
        stop_reason = "solution found"
        self.property_set["layout"] = Layout({v: qubits[k] for k, v in solution.items()})
        for reg in dag.qregs.values():
            self.property_set["layout"].add_register(reg)
    self.property_set["CSPLayout_stop_reason"] = stop_reason