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![An illustration of sets M, X, L and R (after the queries in OPT1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {OPT}_1$$\end{document} have been executed) in the proof of Theorem 5.1](publication/363583570/figure/fig4/AS:11431281115386807@1674875538468/An-illustration-of-setsM-X-L-andR-after-the-queries-in-OPT1documentclass12ptminimal.png)
An illustration of sets M, X, L and R (after the queries in OPT1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {OPT}_1$$\end{document} have been executed) in the proof of Theorem 5.1
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![Possible execution of BAL\documentclass[12pt]{minimal}...](publication/363583570/figure/fig2/AS:11431281115386806@1674875538389/Possible-execution-of-BALdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Bad instance for BAL\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/363583570/figure/fig3/AS:11431281115361218@1674875538420/Bad-instance-for-BALdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
In computing with explorable uncertainty, one considers problems where the values of some input elements are uncertain, typically represented as intervals, but can be obtained using queries. Previous work has considered query minimization in the settings where queries are asked sequentially (adaptive model) or all at once (non-adaptive model). We i...
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Citations
... An algorithm with query ratio 2 for the minimum matroid base problem is also provided in [15]. In [14], algorithms for uncertainty problems are studied in which parallel queries are allowed. Round-competitive algorithms are presented for sorting, selection, and for the minimum value prob-lem. ...
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 here discovery algorithms aiming to minimize the number of queried weights while providing guarantees on the computed solution. We first show in this work 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.
Problems where an algorithm cannot simply access the whole input but needs to obtain information about it using queries arise naturally in many settings. We discuss different aspects of models where an algorithm needs to query the input, and of how the performance of algorithms for such models can be measured. After that, we give some concrete examples of algorithmic settings and results for scenarios where algorithms access the input via queries. Finally, we discuss recent results for the setting of computing with explorable uncertainty with parallel queries and with untrusted predictions.
