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This paper presents stop conditions for solving General Assignment Problems(GAP), in particular for Travel Salesman Problem in an Euclidian 2D space thewell known condition Jordan's simple curve and opposite condition for theKnight Tour Problem. The Jordan's simple curve condition means that a optimaltrajectory must be simple curve, i.e., without crossing but for Knight TourProblem we use the contrary, the feasible trajectory must have crossing in allcities of the tour. The paper presents the algorithms, examples and someresults come from Concorde's Home page. Several problem are studied to depicttheir properties. A classical decision problem SAT is studied in detail.

Complexity and Stop Conditions for NP as General Assignment Problems,  the Travel Salesman Problem in $\mathbb{R}^2$, Knight Tour Problem and  Boolean Satisfiability Problem