Two-dimensional finite impulse response (FIR) filters are an important component in many image and video processing systems. The processing of complex video applications in real time requires high computational power, which can be provided using field programmable gate arrays (FPGAs) due to their inherent parallelism. The most resource-intensive components in computing FIR filters are the multiplications of the folding operation. This work proposes two optimization techniques for high-speed implementations of the required multiplications with the least possible number of FPGA components. Both methods use integer linear programming formulations which can be optimally solved by standard solvers. In the first method, a formulation for the pipelined multiple constant multiplication problem is presented. In the second method, also multiplication structures based on look-up tables are taken into account. Due to the low coefficient word size in video processing filters of typically 8 to 12 bits, an optimal solution is found for most of the filters in the benchmark used. A complexity reduction of 8.5% for a Xilinx Virtex 6 FPGA could be achieved compared to state-of-the-art heuristics.
In this article, we investigate bilevel programming problems with discrete lower level and continuous upper level problems. We will analyse the structure of these problems and discuss both the optimistic and the pessimistic solution approach. Since neither the optimistic nor the pessimistic solution functions are in general lower semicontinuous, we introduce weak solution function. By using these functions we are able to discuss optimality conditions for local and global optimality.
Abstract. Given a graph G = (V, E) with edge weights we ∈ R, the optimum cooperation problem consists in determining a partition of the graph that maximizes the sum of weights of the edges with nodes in the same class plus the number of the classes of the partition. The problem is also known in the literature as the optimum attack problem in networks. Furthermore, a relevant physics application exists. In this work, we present a fast exact algorithm for the optimum cooperation problem. Algorithms known in the literature require |V | − 1 minimum cut computations in a corresponding network. By theoretical considerations and appropriately designed heuristics, we considerably reduce the numbers of minimum cut computations that are necessary in practice. We show the effectiveness of our method by presenting results on instances coming from the physics application. Furthermore, we analyze the structure of the optimal solutions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.