Sorting in c log n parallel steps
Combinatorica
On a Class of Rearrangeable Networks
IEEE Transactions on Computers
Novel sorting network-based architectures for rank order filters
IEEE Transactions on Very Large Scale Integration (VLSI) Systems - Special issue on low-power design
A generalized pipelined median filter network
Signal Processing
FPGA '98 Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Evolution of Non-Deterministic Incremental Algorithms as a New Approach for Search in State Spaces
Proceedings of the 6th International Conference on Genetic Algorithms
A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II
PPSN VI Proceedings of the 6th International Conference on Parallel Problem Solving from Nature
ASIAN '96 Proceedings of the Second Asian Computing Science Conference on Concurrency and Parallelism, Programming, Networking, and Security
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Sorting Networks with Applications to Hierarchical Optical Interconnects
ICPPW '01 Proceedings of the 2001 International Conference on Parallel Processing Workshops
A generalization of the divide-sort-merge strategy for sorting networks
A generalization of the divide-sort-merge strategy for sorting networks
Bit-serial architecture for rank order and stack filters
Integration, the VLSI Journal
UberFlow: a GPU-based particle engine
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
The Estimation of Distributions and the Minimum Relative Entropy Principle
Evolutionary Computation
Marleda: effective distribution estimation through markov random fields
Marleda: effective distribution estimation through markov random fields
A (fairly) simple circuit that (usually) sorts
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Sorting networks and their applications
AFIPS '68 (Spring) Proceedings of the April 30--May 2, 1968, spring joint computer conference
An economical construction for sorting networks
AFIPS '74 Proceedings of the May 6-10, 1974, national computer conference and exposition
Intrinsic evolution of sorting networks: a novel complete hardware implementation for FPGAs
ICES'05 Proceedings of the 6th international conference on Evolvable Systems: from Biology to Hardware
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Sorting networks are an interesting class of parallel sorting algorithms with applications in multiprocessor computers and switching networks. They are built by cascading a series of comparison-exchange units called comparators. Minimizing the number of comparators for a given number of inputs is a challenging optimization problem. This paper presents a two-pronged approach called Symmetry and Evolution based Network Sort Optimization (SENSO) that makes it possible to scale the solutions to networks with a larger number of inputs than previously possible. First, it uses the symmetry of the problem to decompose the minimization goal into subgoals that are easier to solve. Second, it minimizes the resulting greedy solutions further by using an evolutionary algorithm to learn the statistical distribution of comparators in minimal networks. The final solutions improve upon half-century of results published in patents, books, and peer-reviewed literature, demonstrating the potential of the SENSO approach for solving difficult combinatorial problems.