Proceedings of the 2001 international symposium on Symbolic and algebraic computation
On Radiocoloring Hierarchically Specified Planar Graphs: PSPACE-Completeness and Approximations
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Towards a Predictive Computational Complexity Theory
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
An SDS modeling approach for simulation-based control
WSC '05 Proceedings of the 37th conference on Winter simulation
Model-checking hierarchical structures
Journal of Computer and System Sciences
Fixpoint logics on hierarchical structures
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
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We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in [T. Lengauer, J. Assoc. Comput. Mach., 36(1989), pp. 474--509] or are specified by one-dimensional finite narrow periodic specifications as in [E. Wanke, Paths and cycles in finite periodic graphs, in Lecture Notes in Comp. Sci. 711, Springer-Verlag, New York, 1993, pp. 751--760]. We show that, for most of the problems $\Pi$ considered when specified using k-level-restricted hierarchical specifications or k-narrow periodic specifications, the following hold. 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 $(1 + \epsilon) \rho$. $\Pi$ has a polynomial time approximation scheme when restricted to planar instances. These are the first polynomial time approximation schemes for PSPACE-hard hierarchically or periodically specified problems. Since several of the problems considered are PSPACE-hard, our results provide the first examples of natural PSPACE-hard optimization problems that have polynomial time approximation schemes. This answers an open question in Condon et al.\ [Chicago J. Theoret. Comput. Sci., 1995, Article 4].