The alternating basis algorithm for assignment problems

Barr, Ronald E.; Glover, Fred; Klingman, Darwin

doi:10.1007/bf01584319

Cited by 133 publications

(64 citation statements)

References 9 publications

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“…As a final comparison with existing methodology it is worth observing that the computation time of Table 1 [3,7] and 0.38 to 0.90secs on an IBM 370/168 [12]. Making an adjustment for the advantage in speed of the IBM 370 over the CDC 6600 we conclude that our time is comparable ([14] gives an advantage in speed of 5 to 6 for the IBM 370 over the CDC 6600 for network problems although there has been some question on the accuracy of this figure).…”

Section: Combination With the Hungarian Method--computational Resultsmentioning

confidence: 99%

“…It seems that the currently most popular solution methods for the assignment problem are specialized forms of the simplex method [3][4][5] and versions of Kuhn's Hungarian method [6--8]. There has been some controversy regarding the relative merits of simplex codes and primal-dual (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…The computational complexity of many of the existing codes is unknown and in fact some of these codes [3,6] The purpose of this paper is to propose a new method for solving the assignment problem. We show in Section 3 that the worst case complexity of the pure form of the method for full dense, all integer, N × N problems with the elements of the assignment matrix taking values in the interval [0, R] is O(N 3) + O(RN2).…”

Section: Introductionmentioning

confidence: 99%

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A new algorithm for the assignment problem

Bertsekas

1981

Mathematical Programming

246

187

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We propose a new algorithm for the classical assignment problem. The algorithm resembles in some ways the Hungarian method but differs substantially in other respects. The average computational complexity of an efficient implementation of the algorithm seems to be considerably better than the one of the Hungarian method. In a large number of randomly generated problems the algorithm has consistently outperformed an efficiently coded version of the Hungarian method by a broad margin. The factor of improvement increases with the problem dimension N and reaches an order of magnitude for N equal to several hundreds.

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Section: Combination With the Hungarian Method--computational Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A new algorithm for the assignment problem

Bertsekas

1981

Mathematical Programming

246

187

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“…It is also of interest that, for the assignment problem, the "strongly feasible bases" of Cunningham [1976Cunningham [ , 1979 and the "alternating bases" of Barr et al [1977] are, in my terminology, nothing but bases whose signature is always (1, 2, 2, *. .…”

Section: Believe It or Not Yet Another Approach To The Assignment Prmentioning

confidence: 99%

Signature Methods for the Assignment Problem

Balinski

1985

Operations Research

119

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.INFORMS is collaborating with JSTOR to digitize, preserve and extend access to Operations Research.

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“…There has also been a plethora of algorithms for the assignment problem in the thirty five years since Kuhn's original proposal; for a representative but incomplete sample, see [Ba185], [Bal86], [BGK77], [Ber81], [CMT88], [Der85], [Eng82], [GGK82], [Gol85], [Hal56], [Hun83], [JoV87], [McG83], [Mun56], and [Tho81]. All of these methods are based on iterative improvement of some cost function; for example a primal cost (as in primal simplex methods), or a dual cost (as in Hungarian-like methods, in dual simplex methods, and in relaxation methods).…”

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confidence: 99%

The Auction Algorithm for Assignment and Other Network Flow Problems

Bertsekas¹

1991

New Trends in Systems Theory

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This is a tutorial presentation of the auction algorithm, an intuitive method for solving the classical assignment problem. The algorithm outperforms substantially its main competitors for important types of problems, both in theory and in practice, and is also naturally well suited for parallel computation. We derive the algorithm from first principles, we explain its computational properties, and we discuss its extensions to transportation and transhipment problems.

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The alternating basis algorithm for assignment problems

Cited by 133 publications

References 9 publications

A new algorithm for the assignment problem

A new algorithm for the assignment problem

Signature Methods for the Assignment Problem

The Auction Algorithm for Assignment and Other Network Flow Problems

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