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The complexity of controlled selection

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Automata, Languages and Programming (ICALP 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 372))

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Abstract

We identify a class of problems, called controlled selection problems, and study their complexity. A controlled selection problem involves a random selection of a sample from a large set subject to certain structural constraints. The structural constraints model some desired relationships among the elements of the set, which we want to preserve under random selection. For example, the set may be divided into equivalence classes and we may want to ensure that not too many elements are chosen from the same class, or the set may correspond to vertices of a graph and we may want to ensure that the sample does not induce a cycle. Controlled selection problems arise in many disciplines, including statistics, mathematical programming, combinatorial algorithms, and resource allocation. This is the first attempt to unify them. We develop techniques for determining the complexity of controlled selection problems given the structural constraints. We use these techniques to determine the complexity of many types of controlled selection problems. We show that a controlled selection problem is polynomial-time reducible to the problem of finding a maximum weight sample satisfying the structural constraints. We also show that a general reduction in the opposite direction would imply that one-way functions do not exist. In contrast, we show that most natural controlled selection problems have the same complexity (within polynomial time) as the problem of finding a maximum weight sample satisfying the structural constraints. We also present efficient algorithms for several controlled selection problems.

Supported in part by an NSF Presidential Young Investigator Award (grant DCR-8451397), with matching funds from AT&T.

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Author information

Authors and Affiliations

  1. Computer Science Department, University of Wisconsin, 53706, Madison, Wisconsin

    Kirk Pruhs

  2. Computer Science Department, University of Arizona, 85721, Tucson, Arizona

    Udi Manber

Authors
  1. Kirk Pruhs
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  2. Udi Manber
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Editor information

Giorgio Ausiello Mariangiola Dezani-Ciancaglini Simonetta Ronchi Della Rocca

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© 1989 Springer-Verlag Berlin Heidelberg

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Pruhs, K., Manber, U. (1989). The complexity of controlled selection. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds) Automata, Languages and Programming. ICALP 1989. Lecture Notes in Computer Science, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035791

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  • DOI: https://doi.org/10.1007/BFb0035791

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51371-1

  • Online ISBN: 978-3-540-46201-9

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