Sorting networks: To the end and back again

Codish, Michael; Cruz-Filipe, Luís; Ehlers, Thorsten; Müller, Mike; Schneider–Kamp, Peter

doi:10.1016/j.jcss.2016.04.004

Cited by 24 publications

(33 citation statements)

References 21 publications

(67 reference statements)

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“…Optimizing sorting networks for small inputs is an active research area in parallel programming. Knuth [60] and later Codish et al [61] gave networks for sorting up to 17 numbers that were later shown to be optimal in depth, and up to η ≤ 10 also optimal in the number of comparators. Optimizations for up to 20 inputs have recently been achieved, see Table 1 in [61].…”

Section: Resource Analysis Of Quantum Sorting Networkmentioning

confidence: 99%

“…Knuth [60] and later Codish et al [61] gave networks for sorting up to 17 numbers that were later shown to be optimal in depth, and up to η ≤ 10 also optimal in the number of comparators. Optimizations for up to 20 inputs have recently been achieved, see Table 1 in [61]. In such optimizations one typically distinguishes between the optimal depth problem and the problem of minimizing the overall number of comparators.…”

Section: Resource Analysis Of Quantum Sorting Networkmentioning

confidence: 99%

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Improved techniques for preparing eigenstates of fermionic Hamiltonians

et al. 2018

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Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation. First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing the initial states required for simulation of fermions in first quantization. This is an exponential improvement over the previous state-of-the-art. Next, we show how to reduce the overhead due to repeated state preparation in phase estimation when the goal is to prepare the ground state to high precision and one has knowledge of an upper bound on the ground state energy that is less than the excited state energy (often the case in quantum chemistry). Finally, we explain how one can perform the time evolution necessary for the phase estimation based preparation of Hamiltonian eigenstates with exactly zero error by using the recently introduced qubitization procedure.

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Section: Resource Analysis Of Quantum Sorting Networkmentioning

confidence: 99%

Section: Resource Analysis Of Quantum Sorting Networkmentioning

confidence: 99%

Improved techniques for preparing eigenstates of fermionic Hamiltonians

et al. 2018

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“…The previous lemma leads to the following result: The graph in figure 2 has only four perfect matchings: (2,1,3,4,5), (3,1,2,4,5), (2,1,3,5,4), (3,1,2,5,4). So, when testing subsumption, instead of verifying 5!…”

Section: Enumerating Perfect Matchingsmentioning

confidence: 96%

“…The last results for parallel sorting networks are for 17 to 20 inputs and are given in [8], [5]. On the other side, the paper [6] proved the optimality in size for the case n = 9 and n = 10.…”

mentioning

confidence: 95%

An Improved Subsumption Testing Algorithm for the Optimal-Size Sorting Network Problem

Frasinaru

Raschip

2019

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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In this paper a new method for checking the subsumption relation for the optimalsize sorting network problem is described. The new approach is based on creating a bipartite graph and modelling the subsumption test as the problem of enumerating all perfect matchings in this graph. Experiments showed significant improvements over the previous approaches when considering the number of subsumption checks and the time needed to find optimal-size sorting networks. We were able to generate all the complete sets of filters for comparator networks with 9 channels, confirming that the 25-comparators sorting network is optimal. The running time was reduced more than 10 times, compared to the state-of-the-art result described in [6].

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“…Domain-specific techniques such as mathematically designing the prefix layers [7,8] or utilizing certain symmetries [40] were not used.…”

Section: Representationmentioning

confidence: 99%

Enhanced optimization with composite objectives and novelty pulsation

Shahrzad

Hodjat

Dollé

et al. 2019

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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An important benefit of multi-objective search is that it maintains a diverse population of candidates, which helps in deceptive problems in particular. Not all diversity is useful, however: candidates that optimize only one objective while ignoring others are rarely helpful. A recent solution is to replace the original objectives by their linear combinations, thus focusing the search on the most useful tradeoffs between objectives. To compensate for the loss of diversity, this transformation is accompanied by a selection mechanism that favors novelty. This paper improves this approach further by introducing novelty pulsation, i.e. a systematic method to alternate between novelty selection and local optimization. In the highly deceptive problem of discovering minimal sorting networks, it finds state-of-the-art solutions significantly faster than before. In fact, our method so far has established a new world record for the 20-line sorting network with 91 comparators. In the real-world problem of stock trading, it discovers solutions that generalize significantly better on unseen data. Composite Novelty Pulsation is therefore a promising approach to solving deceptive real-world problems through multi-objective optimization.

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Sorting networks: To the end and back again

Cited by 24 publications

References 21 publications

Improved techniques for preparing eigenstates of fermionic Hamiltonians

Improved techniques for preparing eigenstates of fermionic Hamiltonians

An Improved Subsumption Testing Algorithm for the Optimal-Size Sorting Network Problem

Enhanced optimization with composite objectives and novelty pulsation

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