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Proceedings of the 38th annual Design Automation Conference
Exploiting general coefficient representation for the optimal sharing of partial products in MCMs
SBCCI '06 Proceedings of the 19th annual symposium on Integrated circuits and systems design
Multiplierless multiple constant multiplication
ACM Transactions on Algorithms (TALG)
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient shift-adds design of digit-serial multiple constant multiplications
Proceedings of the 21st edition of the great lakes symposium on Great lakes symposium on VLSI
Design of low-power multiple constant multiplications using low-complexity minimum depth operations
Proceedings of the 21st edition of the great lakes symposium on Great lakes symposium on VLSI
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ACM Transactions on Design Automation of Electronic Systems (TODAES)
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ACM Transactions on Design Automation of Electronic Systems (TODAES)
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Proceedings of the International Conference on Computer-Aided Design
SIREN: a depth-first search algorithm for the filter design optimization problem
Proceedings of the 23rd ACM international conference on Great lakes symposium on VLSI
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IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
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This article addresses the multiplication of one data sample with multiple constants using addition/subtraction and shift operations, i.e., the multiple constant multiplications (MCM) operation. In the last two decades, many efficient algorithms have been proposed to implement the MCM operation using the fewest number of addition and subtraction operations. However, due to the NP-hardness of the problem, almost all the existing algorithms have been heuristics. The main contribution of this article is the proposal of an exact depth-first search algorithm that, using lower and upper bound values of the search space for the MCM problem instance, finds the minimum solution consuming less computational resources than the previously proposed exact breadth-first search algorithm. We start by describing the exact breadth-first search algorithm that can be applied on real mid-size instances. We also present our recently proposed approximate algorithm that finds solutions close to the minimum and is able to compute better bounds for the MCM problem. The experimental results clearly indicate that the exact depth-first search algorithm can be efficiently applied to large size hard instances that the exact breadth-first search algorithm cannot handle and the heuristics can only find suboptimal solutions.