11. These problems may be analyzed using graph-theoretic methods, by dynamic programming, or by integer programming . 12. "Optimal " register allocation algorithms based on Integer Programming have been developed by Goodwin and Wilken for regular architectures. 13. In pure integer programming problems, the feasible set is the set of integers ( or some subset thereof ). 14. Tayur's work on integer programming using Gr�bner basis was a finalist for the Frederick W . Lanchester Prize. 15. MINTO is a software system that solves mixed integer programming problem by a branch and bound algorithm with linear programming relaxations. 16. An integer constraint leads to integer programming and Diophantine equations problems, which may have only a finite number of solutions. 17. Other generalizations include satisfiability for first-and second-order logic, constraint satisfaction problems, 0-1 integer programming . 18. Formulate the edge coloring problem as an integer program and describe their experience using an integer programming solver to edge color graphs. 19. The problem of optimizing E T ( Equation ( ) ) can be easily formulated as an Integer programming ( ILP ). 20. Among his mathematical achievements were founding contributions to the field of integer programming , an active area of research to this day.
