Graphical algorithm for the knapsack problems

Abstract

We consider a modification of dynamic programming algorithm (DPA), which is called as graphical algorithm (GA). For the knapsack problem (KP) it is shown that the time complexity of GA is less than the time complexity of DPA. Moreover, the running time of GA is often essentially reduced. GA can also solve big scale instances and instances, where the parameters are not only positive integer. The paper outlines different methods of parallelizing GA taking into account its main features and advantages to various parallel architectures, in particular by using OpenCL and MPI framework. Experiments show that "hard" instances of KP for GA have correlation pjkwjfor all j, where pjand wjare utility and capacity of item j = 1, 2, ⋯, n. © 2011 Springer-Verlag Berlin Heidelberg.