Approximation Algorithms for PSPACEHard Hierarchically and Periodically Specified Problems
Abstract
We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in \cite{Le89} or are specified by 1dimensional finite narrow periodic specifications as in \cite{Wa93}. We show that, for most of the problems $\Pi$ considered when specified using {\bf klevelrestricted} hierarchical specifications or $k$narrow periodic specifications the following holds: \item Let $\rho$ be any performance guarantee of a polynomial time approximation algorithm for $\Pi$, when instances are specified using standard specifications. Then $\forall \epsilon > 0$, $ \Pi$ has a polynomial time approximation algorithm with performance guarantee $(1 + \epsilon) \rho$. \item $\Pi$ has a polynomial time approximation scheme when restricted to planar instances. \end{romannum} These are the first polynomial time approximation schemes for PSPACEhard hierarchically or periodically specified problems. Since several of the problems considered are PSPACEhard, our results provide the first examples of natural PSPACEhard optimization problems that have polynomial time approximation schemes. This answers an open question in Condon et. al. \cite{CF+93}.
 Publication:

arXiv eprints
 Pub Date:
 September 1998
 DOI:
 10.48550/arXiv.cs/9809064
 arXiv:
 arXiv:cs/9809064
 Bibcode:
 1998cs........9064M
 Keywords:

 Computer Science  Computational Complexity;
 Computer Science  Data Structures and Algorithms;
 F.1.3;
 F.2.2
 EPrint:
 5 Figures, 24 pages