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Greediness is not always a vice: Efficient discovery algorithms for assignment problems

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Title: Greediness is not always a vice: Efficient discovery algorithms for assignment problems
Authors: Duvignau, Romaric, 1989, Gillet, Noël, Klasing, Ralf
Source: SESBC TANDEM: Intelligent hantering av energidata och beslutsfattande i realtid Discrete Applied Mathematics. 378:65-86
Subject Terms: Assignment problem, Discovery algorithms, Query complexity, Greedy algorithms
Description: Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and introduce in this work the “discovery” variant considering edge weights that are not provided as input but must be queried, requiring additional and costly computations. We develop discovery algorithms here to minimize the number of queried weights while providing guarantees on the computed solution. In this work, we first show the inherent challenges of designing discovery algorithms for general assignment problems. We then provide and analyze several efficient greedy algorithms that can make use of natural assumptions about the order in which the nodes are processed by the algorithms. Our motivations for exploring this problem stem from finding practical solutions to a variation of maximum weight matching in bipartite hypergraphs, a problem recently emerging in the formation of peer-to-peer energy-sharing communities.
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  Data: Greediness is not always a vice: Efficient discovery algorithms for assignment problems
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  Data: <searchLink fieldCode="AR" term="%22Duvignau%2C+Romaric%22">Duvignau, Romaric</searchLink>, 1989<br /><searchLink fieldCode="AR" term="%22Gillet%2C+Noël%22">Gillet, Noël</searchLink><br /><searchLink fieldCode="AR" term="%22Klasing%2C+Ralf%22">Klasing, Ralf</searchLink>
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  Data: <i>SESBC TANDEM: Intelligent hantering av energidata och beslutsfattande i realtid Discrete Applied Mathematics</i>. 378:65-86
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  Data: Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and introduce in this work the “discovery” variant considering edge weights that are not provided as input but must be queried, requiring additional and costly computations. We develop discovery algorithms here to minimize the number of queried weights while providing guarantees on the computed solution. In this work, we first show the inherent challenges of designing discovery algorithms for general assignment problems. We then provide and analyze several efficient greedy algorithms that can make use of natural assumptions about the order in which the nodes are processed by the algorithms. Our motivations for exploring this problem stem from finding practical solutions to a variation of maximum weight matching in bipartite hypergraphs, a problem recently emerging in the formation of peer-to-peer energy-sharing communities.
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      – SubjectFull: Assignment problem
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      – SubjectFull: Query complexity
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