Accelerating the knapsack problem on GPUs

Abstract: The knapsack problem manifests itself in many domains like cryptography, financial domain and bio-informatics. Knapsack problems are often inside optimization loops in system-level design and analysis of embedded systems as well. Given a set of items, each associated with a profit and a weight, the knapsack problem deals with how to choose a subset of items such that the profit is maximized and the total weight of the chosen items is less than the capacity of the knapsack. There exists several variants and extensions of this knapsack problem. In this thesis, we focus on the multiple-choice knapsack problem, where the items are grouped into disjoint classes. However, the multiple-choice knapsack problem is known to be NP-hard. While many different heuristics and approximation schemes have been proposed to solve the problem in polynomial-time, such techniques do not return the optimal solution. A dynamic programming algorithm to solve the problem optimally is known, but has a pseudo-polynomial running time. This leads to high running times of tools in various application domains where knapsack problems must be solved. Many system-level design tools in the embedded systems domain, in particular, would suffer from high running when such a knapsack problem must be solved inside a larger optimization loop. To mitigate the high running times of such algorithms, in this thesis, we propose a GPU-based technique to solve the multiple-choice knapsack problem. We study different approaches to map the dynamic programming algorithm on the GPU and compare their performance in terms of the running times. We employ GPU specific methods to further improve the running times like exploiting the GPU on-chip shared memory. Apart from results on synthetic test-cases, we also demonstrate the applicability of our technique in practice by considering a case-study from system-level design. Towards this, we consider the problem of instruction-set selection for customizable processors.