Multidimensional assignment problem: Difference between revisions

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{{Short description|Generalization of linear assignment problem from two to multiple dimensions}}

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The '''multidimensional assignment problem''' is a fundamental [[combinatorial optimization]] problem which was introduced by Pierskalla<ref name="Pier68">{{cite journal |last=Pierskalla |first=William P. |title=Letter to the Editor—The Multidimensional Assignment Problem | journal=Operations Research 16(2) |publisher=INFORMS |date=1968 |volume=16 |issue=2 |page=422-431 |doi=10.1287/opre.16.2.422 |url=https://pubsonline.informs.org/doi/abs/10.1287/opre.16.2.422}}</ref>. This problem can be seen as a generalization of the linear [[assignment problem]].<ref name="Pasi21">{{Cite arXiv|last=Kammerdiner|first=Alla|last2=Semenov|first2=Alexander|last3=Pasiliao|first3=Eduardo |date=2021|title=Multidimensional Assignment Problem for multipartite entity resolution|eprint=2112.03346}}</ref> In words, the problem can be described as follows:

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The problem found application in many domains:

*[[Scheduling (production processes)]] <ref name="Pier68" />

*[[Data fusion|Multi-sensor data fusion]] <ref>{{Cite journal|last=Poore|first=Aubrey B.|date=1994|title=Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking|journal=Computational Optimization and Applications|volume=3|issue=1|pages=27-57|doi=10.1007/BF01299390}}</ref>

*[[Record linkage|Record linkage or multipartite entity resolution]] <ref name="Pasi21" />

*[[Particle physics|Elementary particle physics]] <ref>{{Cite journal|last=Pusztaszeri|first=Jean-François|last2=Rensing|first2=Paul E.|last3=Liebling|first3=Thomas M.|date=1996|title=Tracking elementary particles near their primary vertex: a combinatorial approach|journal=Journal of Global Optimization|volume=9|issue=1|pages=41-64|doi=10.1007/BF00121750}}</ref>

*[[Medical alarm|Fall detection in elderly with small wearable devices]]<ref>{{Cite journal|last=Kammerdiner|first=Alla R.|last2=Guererro|first2=Andre N.|date=2019|title=Data-driven combinatorial optimization for sensor-based assessment of near falls|url=http://link.springer.com/10.1007/s10479-017-2585-1|journal=Annals of Operations Research|language=en|volume=276|issue=1-2|pages=137–153|doi=10.1007/s10479-017-2585-1|issn=0254-5330}}</ref>

== References ==

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