The Hungarian method for the assignment problem

Kuhn, Harold W.

doi:10.1002/nav.3800020109

Cited by 9,177 publications

(1,833 citation statements)

References 6 publications

(1 reference statement)

Supporting

Mentioning

1,507

Contrasting

Unclassified

Order By: Relevance

“…This cost function needs to be minimized in order to find the EMD. This problem is generally known as the transportation problem (Cha and Srihari, 2002;Rubner et al, 2002), and many different specific solutions exist such as the Hungarian method (Kuhn, 1955) or the simplex method. These methods find the minimal distance over which the mass needs to be transported, such that the EMD can be found by multiplying the mass transported by the distance it needs to be moved.…”

Section: Assessment Of the Resulting Probability Distribution Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Copula-based downscaling of spatial rainfall: a proof of concept

Berg

Vandenberghe

Baets

et al. 2011

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

Abstract. Fine-scale rainfall data is important for many hydrological applications. However, often the only data available is at a coarse scale. To bridge this gap in resolution, stochastic disaggregation methods can be used. Such methods generally assume that the distribution of the field is stationary, i.e. the distribution for the entire (fine-scale) field is the same as the distribution of a smaller region within the field. This assumption is generally incorrect and we provide a proof of concept of a method to estimate the distribution of a smaller region. In this method, a copula is used to construct a bivariate distribution describing the relation between the scales. This distribution is then used to estimate the distribution of the fine-scale rainfall within a single coarse-scale pixel, by conditioning on the coarse-scale rainfall depth.

show abstract

Section: Assessment Of the Resulting Probability Distribution Functionsmentioning

confidence: 99%

Section: Construction Of the Intermittence Modelmentioning

confidence: 99%

Copula-based downscaling of spatial rainfall: a proof of concept

Berg

Vandenberghe

Baets

et al. 2011

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

show abstract

“…Several approaches were proposed including NeRoSim (Banjade et al, 2015), UBC-Cubes (Agirre et al, 2015) and Exb-Thermis (Hänig et al, 2015). For the task of alignment, these submissions used approaches based on monolingual aligner using word similarity and contextual features (Md Arafat Sultan and Summer, 2014), JACANA that uses phrase based semimarkov CRFs (Yao and Durme, 2015) and Hungarian Munkers algorithm (Kuhn and Yaw, 1955). Other popular approaches for mono-lingual alignment include two-stage logistic-regression based aligner (Md Arafat Sultan and Summer, 2015), techniques based on edit rate computation such as (lien Maxe Anne Vilnat, 2011) and TER-Plus (Snover et al, 2009).…”

Section: Introduction and Related Workmentioning

confidence: 99%

IISCNLP at SemEval-2016 Task 2: Interpretable STS with ILP based Multiple Chunk Aligner

Tekumalla¹,

Jat²

2016

Proceedings of the 10th International Workshop on Semantic Evaluation (SemEval-2016)

View full text Add to dashboard Cite

Interpretable semantic textual similarity (iSTS) task adds a crucial explanatory layer to pairwise sentence similarity. We address various components of this task: chunk level semantic alignment along with assignment of similarity type and score for aligned chunks with a novel system presented in this paper. We propose an algorithm, iMATCH, for the alignment of multiple non-contiguous chunks based on Integer Linear Programming (ILP). Similarity type and score assignment for pairs of chunks is done using a supervised multiclass classification technique based on Random Forrest Classifier. Results show that our algorithm iMATCH has low execution time and outperforms most other participating systems in terms of alignment score. Of the three datasets, we are top ranked for answerstudents dataset in terms of overall score and have top alignment score for headlines dataset in the gold chunks track.

show abstract

“…Among many of these problems, two well-known discrete combinatorial optimization problems are: Assignment problem (AP) and Traveling Salesman problem (TSP). A generic Assignment Problem [1][2][3] is defined on a n × n bipartite matrix representing a system consisting of n subjects, each of which is characterized by a n-dim vector of cost of performing n different tasks. While Traveling Salesman problem is defined generically on a symmetric distance matrix between all "cities."…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Meliorates Computing and Robustness in Discrete Combinatorial Optimization Problems

Hsieh

Fujii

Hsieh

2016

Front. Appl. Math. Stat.

View full text Add to dashboard Cite

Discrete combinatorial optimization problems in the real world are typically defined via an ensemble of potentially high dimensional measurements pertaining to all subjects of a system under study. We point out that such a data ensemble in fact embeds with system's information content that is not directly used in defining the combinatorial optimization problems. Can machine learning algorithms extract such information content and make combinatorial optimizing tasks more efficient? Would such algorithmic computations bring new perspectives into this classic topic of Applied Mathematics and Theoretical Computer Science? We show that answers to both questions are positive. One key reason is due to permutation invariance. That is, the data ensemble of subjects' measurement vectors is permutation invariant when it is represented through a subject-vs.-measurement matrix. An unsupervised machine learning algorithm, called Data Mechanics (DM), is applied to find optimal permutations on row and column axes such that the permuted matrix reveals coupled deterministic and stochastic structures as the system's information content. The deterministic structures are shown to facilitate geometry-based divide-and-conquer scheme that helps optimizing task, while stochastic structures are used to generate an ensemble of mimicries retaining the deterministic structures, and then reveal the robustness pertaining to the original version of optimal solution. Two simulated systems, Assignment problem and Traveling Salesman problem, are considered. Beyond demonstrating computational advantages and intrinsic robustness in the two systems, we propose brand new robust optimal solutions. We believe such robust versions of optimal solutions are potentially more realistic and practical in real world settings.

show abstract

The Hungarian method for the assignment problem

Cited by 9,177 publications

References 6 publications

Copula-based downscaling of spatial rainfall: a proof of concept

Copula-based downscaling of spatial rainfall: a proof of concept

IISCNLP at SemEval-2016 Task 2: Interpretable STS with ILP based Multiple Chunk Aligner

Machine Learning Meliorates Computing and Robustness in Discrete Combinatorial Optimization Problems

Contact Info

Product

Resources

About