A Graphical Approach for Solving NP-Hard Combinatorial Problems

In this paper we consider a graphical realization of dynamic programming. The concept is discussed on the partition and knapsack problems. In contrast to dynamic programming, the new algorithm can also treat problems with non-integer data without necessary transformations of the corresponding problem. We compare the proposed method with existing algorithms for these problems on small-size instances of the partition problem with n ≤ 10 numbers. For almost all instances, the new algorithm considers on average substantially less ”stages” than the dynamic programming algorithm.