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The Update Complexity of Selection and Related Problems.

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Title: The Update Complexity of Selection and Related Problems.
Authors: Gupta, Manoj1 gmanoj@cse.iitd.ernet.in, Sabharwal, Yogish2 ysabharwal@in.ibm.com, Sen, Sandeep1 ssen@cse.iitd.ernet.in
Source: Theory of Computing Systems. Jul2016, Vol. 59 Issue 1, p112-132. 21p.
Subjects: Ranking (Statistics), Selection theorems, Uncertainty, Input-output analysis, Combinatorial set theory, Management
Abstract: We present a framework for computing with input data specified by intervals, representing uncertainty in the values of the input parameters. To compute a solution, the algorithm can query the input parameters that yield more refined estimates in the form of sub-intervals and the objective is to minimize the number of queries. The previous approaches address the scenario where every query returns an exact value. Our framework is more general as it can deal with a wider variety of inputs and query responses and we establish interesting relationships between them that have not been investigated previously. Although some of the approaches of the previous restricted models can be adapted to the more general model, we require more sophisticated techniques for the analysis and we also obtain improved algorithms for the previous model. We address selection problems in the generalized model and show that there exist 2-update competitive algorithms that do not depend on the lengths or distribution of the sub-intervals and hold against the worst case adversary. We also obtain similar bounds on the competitive ratio for the MST problem in graphs. [ABSTRACT FROM AUTHOR]
Copyright of Theory of Computing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="DE" term="%22Ranking+%28Statistics%29%22">Ranking (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Selection+theorems%22">Selection theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Uncertainty%22">Uncertainty</searchLink><br /><searchLink fieldCode="DE" term="%22Input-output+analysis%22">Input-output analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+set+theory%22">Combinatorial set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Management%22">Management</searchLink>
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  Data: We present a framework for computing with input data specified by intervals, representing uncertainty in the values of the input parameters. To compute a solution, the algorithm can query the input parameters that yield more refined estimates in the form of sub-intervals and the objective is to minimize the number of queries. The previous approaches address the scenario where every query returns an exact value. Our framework is more general as it can deal with a wider variety of inputs and query responses and we establish interesting relationships between them that have not been investigated previously. Although some of the approaches of the previous restricted models can be adapted to the more general model, we require more sophisticated techniques for the analysis and we also obtain improved algorithms for the previous model. We address selection problems in the generalized model and show that there exist 2-update competitive algorithms that do not depend on the lengths or distribution of the sub-intervals and hold against the worst case adversary. We also obtain similar bounds on the competitive ratio for the MST problem in graphs. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Theory of Computing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Selection theorems
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              Text: Jul2016
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