An Ising model mapping to solve rectangle packing problem

Terada, Kotaro; Oku, Daisuke; Kanamaru, Sho; Tanaka, Shu; Hayashi, Masato; Yamaoka, Masanao; Yanagisawa, Masao; Togawa, Nozomu

doi:10.1109/vlsi-dat.2018.8373233

Cited by 25 publications

(14 citation statements)

References 6 publications

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“…In Eq. (17), the lowest value of H NPP becomes zero. When H NPP is zero, the set of positive numbers can be partitioned into two disjoint subsets, in which the sum of each subset is the same.…”

Section: Number Partition Problemmentioning

confidence: 90%

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How to Reduce the Bit-Width of an Ising Model by Adding Auxiliary Spins

Oku

Tawada

Tanaka

et al. 2022

IEEE Trans. Comput.

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Section: Number Partition Problemmentioning

confidence: 90%

“…Phase 1 itself is a very challenging task. However, the Ising model or quadratic unconstrained binary optimization (QUBO) model formulations targeted for practical combinatorial optimization problems have been proposed [15], [16], [17], [18], [19]. Especially, PyQUBO is a software package that supports these formulations [19].…”

Section: Introductionmentioning

confidence: 99%

How to Reduce the Bit-Width of an Ising Model by Adding Auxiliary Spins

Oku

Tawada

Tanaka

et al. 2022

IEEE Trans. Comput.

Self Cite

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“…CBMs are equivalent to Ising models; therefore, CBMs are also adaptable to combinatorial optimization problems. Many studies were related to Ising models [25], [26] and their hardware implementations [27]- [29] in recent years FIGURE 20: Efficiency of the calculation time because many problems in our society can be expressed as combinatorial optimization problems. Table 10 compares the results of our implementation and related studies.…”

Section: Related Workmentioning

confidence: 99%

FPGA Implementation of Hardware-Oriented Chaotic Boltzmann Machines

2020

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“…Substituting eqs. (19) and (22) into (21) gives (16). The guiding principle of ME design to achieve a high performance in Ising machines is that the intra-ring-coupling strength must be tuned according to eq.…”

Section: Types Of Minor-embeddingmentioning

confidence: 99%

Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

2020

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We propose a novel type of minor-embedding (ME) in simulated-annealing-based Ising machines. The Ising machines can solve combinatorial optimization problems. Many combinatorial optimization problems are mapped to find the ground (lowest-energy) state of the logical Ising model. When connectivity is restricted on Ising machines, ME is required for mapping from the logical Ising model to a physical Ising model, which corresponds to a specific Ising machine. Herein we discuss the guiding principle of ME design to achieve a high performance in Ising machines. We derive the proposed ME based on a theoretical argument of statistical mechanics. The performance of the proposed ME is compared with two existing types of MEs for different benchmarking problems. Simulated annealing shows that the proposed ME outperforms existing MEs for all benchmarking problems, especially when the distribution of the degree in a logical Ising model has a large standard deviation. This study validates the guiding principle of using statistical mechanics for ME to realize fast and high-precision solvers for combinatorial optimization problems.

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An Ising model mapping to solve rectangle packing problem

Cited by 25 publications

References 6 publications

How to Reduce the Bit-Width of an Ising Model by Adding Auxiliary Spins

How to Reduce the Bit-Width of an Ising Model by Adding Auxiliary Spins

FPGA Implementation of Hardware-Oriented Chaotic Boltzmann Machines

Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

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