Subexponential Time and Fixed-parameter Tractability: Exploiting the Miniaturization Mapping

Recently it has been shown that the miniaturization mapping ℳ faithfully translates bexponential parameterized complexity into (unbounded) parameterized complexity. We determine the pre-images under ℳ of various (classes of) problems. For many parameterized problems whose underlying classical problem is in NP we show that the pre-images coincide with natural reparameterizations that take into account the amount of non-determinism needed to solve them.

[1]  Jörg Flum,et al.  Model-checking problems as a basis for parameterized intractability , 2004, LICS 2004.

[2]  Jörg Flum,et al.  Parameterized Complexity Theory , 2006, Texts in Theoretical Computer Science. An EATCS Series.

[3]  Jörg Flum,et al.  Bounded Fixed-Parameter Tractability and log2n Nondeterministic Bits , 2004, ICALP.

[4]  John Doner,et al.  Tree Acceptors and Some of Their Applications , 1970, J. Comput. Syst. Sci..

[5]  James W. Thatcher,et al.  Generalized finite automata theory with an application to a decision problem of second-order logic , 1968, Mathematical systems theory.

[6]  Mihalis Yannakakis,et al.  On the Complexity of Database Queries , 1999, J. Comput. Syst. Sci..

[7]  Venkatesh Raman,et al.  Parameterized complexity of finding subgraphs with hereditary properties , 2000, Theor. Comput. Sci..

[8]  Ge Xia,et al.  Tight lower bounds for certain parameterized NP-hard problems , 2004, Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004..

[9]  Jörg Flum,et al.  Bounded fixed-parameter tractability and log2n nondeterministic bits , 2004, J. Comput. Syst. Sci..

[10]  Yijia Chen,et al.  An isomorphism between subexponential and parameterized complexity theory , 2006, 21st Annual IEEE Conference on Computational Complexity (CCC'06).

[11]  Martin Grohe,et al.  Parameterized Complexity and Subexponential Time , 2004 .

[12]  Michael R. Fellows,et al.  Fixed Parameter Tractability and Completeness , 1992, Complexity Theory: Current Research.

[13]  Martin Grohe,et al.  The complexity of first-order and monadic second-order logic revisited , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[14]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .