A low-space algorithm for the subset-sum problem on GPU

Curtis, Vitor Venceslau; Sanches, Carlos Alberto Alonso

doi:10.1016/j.cor.2017.02.006

Cited by 10 publications

(8 citation statements)

References 9 publications

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“…we find that, if the weight matrix W is symmetric and is hollow (i.e. has diagonal of all zeros), then the Hopfield energy can never increase when updating one neuron by (8). Since…”

Section: Qubo-solving With Hopfield Networkmentioning

confidence: 96%

“…There is much work done on parallelization approaches and GPU-assisted computing to solve an adjusted problem statement in which one tries to maximize x∈Y x under the restriction x∈Y x ≤ T . See [8] for a discussion of various algorithms.…”

Section: Related Workmentioning

confidence: 99%

“…A Hopfield network architecture is therefore fully described by a matrix W , a vector θ and a current state s. An update of the network is done via (8), either for all neurons at once or only a subset of neurons.…”

Section: Qubo-solving With Hopfield Networkmentioning

confidence: 99%

See 2 more Smart Citations

Solving Subset Sum Problems using Binary Optimization with Applications in Auditing and Financial Data Analysis

Biesner¹,

Sifa²,

Bauckhage³

2022

Preprint

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<div><br></div><div>Many applications in automated auditing and the analysis and consistency check of financial documents can be formulated in part as the subset sum problem: Given a set of numbers and a target sum, find the subset of numbers that sums up to the target. The problem is NP-hard and classical solving algorithms are therefore not practical to use in real applications. We tackle the problem as a QUBO (quadratic unconstrained binary optimization) problem and show how gradient descent on Hopfield Networks reliably finds solutions for both artificial and real data. We give an outlook for the application of specialized hardware and quantum algorithms.</div>

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“…we find that, if the weight matrix W is symmetric and is hollow (i.e. has diagonal of all zeros), then the Hopfield energy can never increase when updating one neuron by (8). Since…”

Section: Qubo-solving With Hopfield Networkmentioning

confidence: 96%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Solving Subset Sum Problems using Binary Optimization with Applications in Auditing and Financial Data Analysis

Biesner¹,

Sifa²,

Bauckhage³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…It can be proven that this approach gives the correct results. For more advanced algorithm using Dynamic Programming related tools see [2], [3], [4], [5].…”

Section: Approaches From Literaturementioning

confidence: 99%

A FPTAS for the Subset Sum Problem with Real Numbers

Costandin¹

2021

Preprint

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In this paper we study the subset sum problem with real numbers. Starting from the given problem, we formulate a quadratic maximization problem over a polytope which is eventually written as a distance maximization to a fixed point. For solving this, we provide a polynomial algorithm which maximizes the distance to a fixed point over a certain convex set. This convex set is obtained by intersecting the unit hypercube with two relevant half spaces. We show that in case the subset sum problem has a solution, our algorithm gives the correct maximum distance up to an arbitrary chosen precision. In such a case, we show that the obtained maximizer is a solution to the subset sum problem. Therefore, we compute the maximizer and upon analyzing it we can assert the feasibility of the subset sum problem.

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“…Theoretical bounds on the complexity of parallel solving of SSP are obtained in [7][8][9][10][11] for dynamic programming method and in [12] for two-list method. Empirical parallel algorithms of solving SSP by dynamic programming method for CPU and GPU computational models are proposed in [11,13,14]. Empirical parallelizations of two-list method of solving of SSP for GPU and hybrid CPU/GPU computational models are proposed in [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Optimality and Complexity Analysis of a Branch-and-Bound Method in Solving Some Instances of the Subset Sum Problem

Kolpakov

Posypkin

2020

Open Computer Science

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In this paper we study the question of parallelization of a variant of Branch-and-Bound method for solving of the subset sum problem which is a special case of the Boolean knapsack problem. The following natural approach to the solution of this question is considered. At the first stage one of the processors (control processor) performs some number of algorithm steps of solving a given problem with generating some number of subproblems of the problem. In the second stage the generated subproblems are sent to other processors for solving (one subproblem per processor). Processors solve completely the received subproblems and return their solutions to the control processor which chooses the optimal solution of the initial problem from these solutions. For this approach we define formally a model of parallel computing (frontal parallelization scheme) and the notion of complexity of the frontal scheme. We study the asymptotic behavior of the complexity of the frontal scheme for two special cases of the subset sum problem.

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A low-space algorithm for the subset-sum problem on GPU

Cited by 10 publications

References 9 publications

Solving Subset Sum Problems using Binary Optimization with Applications in Auditing and Financial Data Analysis

Solving Subset Sum Problems using Binary Optimization with Applications in Auditing and Financial Data Analysis

A FPTAS for the Subset Sum Problem with Real Numbers

Optimality and Complexity Analysis of a Branch-and-Bound Method in Solving Some Instances of the Subset Sum Problem

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