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Polynomially bounded minimization problems which are hard to approximate

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Automata, Languages and Programming (ICALP 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 700))

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Abstract

Min PB is the class of minimization problems whose objective functions are bounded by a polynomial in the size of the input. We show that there exist several problems which are Min PB-complete with respect to an approximation preserving reduction. These problems are very hard to approximate; in polynomial time they cannot be approximated within nε for some ε>0, where n is the size of the input, provided that P≠NP. In particular, the problem of finding the minimum independent dominating set in a graph, the problem of satisfying a 3-SAT formula setting the least number of variables to one, and the minimum bounded 0–1 programming problem are shown to be Min PB-complete. We also present a new type of approximation preserving reduction that is designed for problems whose approximability is expressed as a function in some size parameter. Using this reduction we obtain good lower bounds on the approximability of the treated problems.

Supported by grants from TFR.

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Authors and Affiliations

  1. Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44, Stockholm, Sweden

    Viggo Kann

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  1. Viggo Kann
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Andrzej Lingas Rolf Karlsson Svante Carlsson

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© 1993 Springer-Verlag Berlin Heidelberg

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Kann, V. (1993). Polynomially bounded minimization problems which are hard to approximate. In: Lingas, A., Karlsson, R., Carlsson, S. (eds) Automata, Languages and Programming. ICALP 1993. Lecture Notes in Computer Science, vol 700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56939-1_61

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  • DOI: https://doi.org/10.1007/3-540-56939-1_61

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56939-8

  • Online ISBN: 978-3-540-47826-3

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