An infeasible (exterior point) simplex algorithm for assignment problems

Paparrizos, Konstantinos

doi:10.1007/bf01586925

Cited by 49 publications

(31 citation statements)

References 12 publications

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“…The number of pivots is again O(n 2 ) but the overall complexity becomes O(n 3 ). Later, Paparrizos [137] designed a purely infeasible simplex algorithm which performs O(n 2 ) pivots and has worst case complexity of O(n 3 ). This algorithm is similar to the algorithm presented in [135] since it starts again with a Balinski tree and visits only strong trees.…”

Section: Definition 34mentioning

confidence: 99%

“…An O(n 3 ) forest algorithm is proposed by Achatz, Kleinschmidt, and Paparrizos [1] and is a more efficient variant of the algorithm proposed by Paparrizos in [137]. The algorithm starts with some basic dual feasible tree rooted at some arbitrary node in V , and constructs a forest by deleting all edges (i, j) where i ∈ V , j ∈ W , and i is the father of j with respect to the usual orientation of the tree which directs all edges away from the root.…”

Section: Forest Algorithmsmentioning

confidence: 99%

See 1 more Smart Citation

Linear Assignment Problems and Extensions

Burkard

Çela

1999

Handbook of Combinatorial Optimization

255

150

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This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems, starting with the assignment polytope and the relationship between assignment and matching problems, and focusing then on deterministic and randomized algorithms, parallel approaches, and the asymptotic behaviour. Further, we describe different applications of assignment problems, ranging from the well know personnel assignment or assignment of jobs to parallel machines, to less known applications, e.g. tracking of moving objects in the space. Finally, planar and axial three-dimensional assignment problems are considered, and polyhedral results, as well as algorithms for these problems or their special cases are discussed. The paper will appear in the Handbook of Combinatorial Optimization to be published by Kluwer Academic Publishers, P. Pardalos and D.-Z. Du, eds.

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Section: Definition 34mentioning

confidence: 99%

Section: Forest Algorithmsmentioning

confidence: 99%

Linear Assignment Problems and Extensions

Burkard

Çela

1999

Handbook of Combinatorial Optimization

255

150

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“…Although the existing linear programming problem algorithms are effective in solving many practical problems, they have to run a long time to find solutions to large scale problems. To overcome this limitation, researchers have proposed some methods for improvement, such as the infeasible exterior point simplex algorithm for assignment problems [3] and the efficient search direction for linear programming problems [4]. These methods reduce the iterative times successfully, but fail to improve the efficiency of iterative process.…”

Section: Introductionmentioning

confidence: 98%

A GPU-Based Parallel Algorithm for Large Scale Linear Programming Problem

et al. 2011

Intelligent Decision Technologies

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Abstract.A GPU-based parallel algorithm to solve large scale linear programming problem is proposed in this research. It aims to improve the computing efficiency when the linear programming problem becomes sufficiently large scale or more complicated. This parallel algorithm, based on Gaussian elimination, uses the GPU (Graphics Processing Unit) for computationally intensive tasks such as basis matrix operation, canonical form transformation and entering variable selection. At the same time, CPU is used to control the iteration. Experimental results show that the algorithm is competitive with CPU algorithm and can greatly reduce the computing time, so the GPU-based parallel algorithm is an effective way to solve large scale linear programming problem.

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“…However, there is still much research being done in order to improve pivoting algorithms. Recently, Paparrizos [2] proposed an exterior point Simplex algorithm that avoids the feasible region; Luh and Tsaih [3] proposed using IPM to replace phase I of the Simplex; Paparrizos et al [4] proposed a di erent approach based on integrating IPM and Simplex methods. The literature presents further relevant Refs.…”

Section: Introductionmentioning

confidence: 99%

An improved initial basis for the Simplex algorithm

Vieira

Lins

2005

Computers & Operations Research

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A lot of research has been done to ÿnd a faster (polynomial) algorithm that can solve linear programming (LP) problems. The main branch of this research has been devoted to interior point methods (IPM). The IPM outperforms the Simplex method in large LPs. However, there is still much research being done in order to improve pivoting algorithms. In this paper, we present a new approach to the problem of improving the pivoting algorithms: instead of starting the Simplex with the canonical basis, we suggest as initial basis a vertex of the feasible region that is much closer to the optimal vertex than the initial solution adopted by the Simplex. By supplying the Simplex with a better initial basis, we were able to improve the iteration number e ciency of the Simplex algorithm in about 33%. ?

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An infeasible (exterior point) simplex algorithm for assignment problems

Cited by 49 publications

References 12 publications

Linear Assignment Problems and Extensions

Linear Assignment Problems and Extensions

A GPU-Based Parallel Algorithm for Large Scale Linear Programming Problem

An improved initial basis for the Simplex algorithm

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