Abstract
We describe how to found and develop the theory of fixed-parameter complexity and hardness in a manner both fully analgous to the classical theory of NP-completeness and much simpler than the original development. We present some recent advance made using this approach.
- J. F. Buss, J. Goldsmith, "Nondeterminism within P," SIAM J. Computing 22 (1993) 560--572. Google ScholarDigital Library
- J. F. Buss, T. Islam, "Simplifying the Weft Hierarchy," Theoretical Computer Science 351 (2006) 303--313. Google ScholarDigital Library
- J. F. Buss, T. Islam, "Algorithms in the Weft Hierarchy," Theory of Computing Systems 41 (2007) 445--457. Google ScholarDigital Library
- J. F. Buss, T. Islam, "The Fixed-Parameter Complexity of Longest-Common-Subsequence and PDA Intersection Problems," in preparation.Google Scholar
- M. Cesati, "The Turing Way to Parameterized Complexity," Journal of Computer and System Sciences 67, 4 (2003) 654--685. Google ScholarDigital Library
- Y. Chen, J. Flum, "Machine Characterization of the Classes of the W hierarchy," in Computer Science Logic: CSL 2003, Lecture Notes in Computer Science 2803, Springer, 2003, pp. 114--127.Google Scholar
- Y. Chen, J. Flum, M. Grohe, "Bounded Nondeterminism and Alternation in Parameterized Complexity Theory," in 18th Ann. IEEE Conf. Computational Complexity, 2003, pp. 18--29.Google Scholar
- Y. Chen, J. Flum, M. Grohe, "Machine-Based Methods in Parameterized Complexity Theory," Theoretical Computer Science 339 (2005) 167--199. Google ScholarDigital Library
- R. G. Downey, M. R. Fellows, "Fixed-Parameter Tractability and Completeness I: Basic Results," SIAM J. Computing 24, 4 (1995) 873--921. Google ScholarDigital Library
- R. G. Downey, M. R. Fellows, "Fixed-Parameter Tractability and Completeness II: On Completeness for W{1}," Theoretical Computer Science 141 (1995) 109--131. Google ScholarDigital Library
- R. G. Downey, M. R. Fellows, Parameterized Complexity, Springer, 1999. Google ScholarDigital Library
- J. Flum, M. Grohe, "Fixed-Parameter Tractability, Definability, and Model-Checking," SIAM J. Computing 31 (2001) 113--145. Google ScholarDigital Library
- J. Flum, M. Grohe, Parameterized Complexity Theory, Springer, 2006. Google ScholarDigital Library
- T. M. Islam, Characterizing Hardness in Parameterized Complexity, Ph.D. thesis, University of Waterloo, 2007. Google ScholarDigital Library
- H. T. Wareham, "The Parameterized Complexity of Intersection and Composition Operations on Sets of Finite-State Automata," International Conference on Implementation and Application of Automata, Lecture Notes in Computer Science 2088, Springer, 2000, pp. 302--310. Google ScholarDigital Library
Index Terms
- The complexity of fixed-parameter problems: guest column
Recommendations
On the complexity of fixed parameter problems
SFCS '89: Proceedings of the 30th Annual Symposium on Foundations of Computer ScienceThe authors address the question of why some fixed-parameter problem families solvable in polynomial time seem to be harder than others with respect to fixed-parameter tractability: whether there is a constant alpha such that all problems in the family ...
Fixed-Parameter Tractability and Completeness I: Basic Results
For many fixed-parameter problems that are trivially soluable in polynomial-time, such as ($k$-)DOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as ($k$-)...
Fixed-parameter complexity in AI and nonmonotonic reasoning
Many relevant intractable problems become tractable if some problem parameter is fixed. However, various problems exhibit very different computational properties, depending on how the runtime required for solving them is related to the fixed parameter ...
Comments