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Optimization Problems in the Polynomial-Time Hierarchy

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Theory and Applications of Models of Computation (TAMC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3959))

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Abstract

This talk surveys work on classifying the complexity and approximability of problems residing in the Polynomial-Time Hierarchy, above the first level. Along the way, we highlight some prominent natural problems that are believed – but not yet known – to be \(\Sigma^p_2\)-complete. We describe how strong inapproximability results for certain \(\Sigma^p_2\) optimization problems can be obtained using dispersers to build error-correcting codes. Finally we adapt a learning algorithm to produce approximation algorithms for these problems.

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Author information

Authors and Affiliations

  1. Computer Science Department, California Institute of Technology, Pasadena, CA, 91125, USA

    Christopher Umans

Authors
  1. Christopher Umans
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Editor information

Editors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, 53706, Madison, WI, USA

    Jin-Yi Cai

  2. School of Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.

    S. Barry Cooper

  3. State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences,  

    Angsheng Li

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© 2006 Springer-Verlag Berlin Heidelberg

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Umans, C. (2006). Optimization Problems in the Polynomial-Time Hierarchy. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_33

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  • DOI: https://doi.org/10.1007/11750321_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34021-8

  • Online ISBN: 978-3-540-34022-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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