1991
DOI: 10.1090/dimacs/004/01
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A dual forest algorithm for the assignment problem

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Cited by 29 publications
(24 citation statements)
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“…. , n Let A be the coefficient matrix of the system of equations (1). Matrix A is totally unimodular , i.e., every square submatrix of A has a determinant of value +1, −1 or 0.…”
Section: Assignmentsmentioning
confidence: 99%
See 1 more Smart Citation
“…. , n Let A be the coefficient matrix of the system of equations (1). Matrix A is totally unimodular , i.e., every square submatrix of A has a determinant of value +1, −1 or 0.…”
Section: Assignmentsmentioning
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%
“…An extension of Balinski's method to other transportation problems has been presented by Kleinschmidt et al [8]. An efficient category of simplex type algorithms for the AP [9][10][11] has been developed. This category is called Exterior Point Simplex Algorithms (EPSAs).…”
Section: Introductionmentioning
confidence: 99%
“…The aim of this paper is to mathematically define test problems, independently of size, which can force the EPSA [11] to perform maximum iterations. In [11] it is proved that the algorithm is bound to perform at most n(n−1) 2 iterations when solving an AP of size n. The overall complexity of this algorithm is O(n 3 ).…”
Section: Introductionmentioning
confidence: 99%
“…Vertices and edges that compose a graph are intuitively depicted and are easily interpreted by the user -student. We present a visualization tool for teaching a specific graph algorithm [2] for the assignment problem, which provides visual and animated representation of the algorithm's execution and its details. From now on this specific algorithm, it will be referenced simply as "algorithm".…”
Section: Introductionmentioning
confidence: 99%