On the computational hardness based on linear FPT-reductions

The notion of linear fpt-reductions has been recently introduced to derive strong computational lower bounds for well-known NP-hard problems. In this paper, we formally investigate the notion of W[t]-hardness under the linear fpt-reduction, and study the structural properties of the corresponding complexity classes. Additional complexity lower bounds on important computational problems are established. Some observations on structural properties of the standard parameterized hierarchy, the W -hierarchy, are also presented.

[1]  Giorgio Gambosi,et al.  Complexity and Approximation , 1999, Springer Berlin Heidelberg.

[2]  Giorgio Ausiello,et al.  Structure Preserving Reductions among Convex Optimization Problems , 1980, J. Comput. Syst. Sci..

[3]  Michael R. Fellows,et al.  FIXED-PARAMETER TRACTABILITY AND COMPLETENESS , 2022 .

[4]  Luca Trevisan,et al.  On the Efficiency of Polynomial Time Approximation Schemes , 1997, Inf. Process. Lett..

[5]  Liming Cai,et al.  The inapproximability of non-NP-hard optimization problems , 2002, Theor. Comput. Sci..

[6]  Robert E. Tarjan,et al.  Finding a Maximum Independent Set , 1976, SIAM J. Comput..

[7]  Liming Cai,et al.  On the existence of subexponential parameterized algorithms , 2003, J. Comput. Syst. Sci..

[8]  Michael R. Fellows,et al.  Parameterized learning complexity , 1993, COLT '93.

[9]  R. Downey,et al.  Parameterized Computational Feasibility , 1995 .

[10]  Michael R. Fellows,et al.  W[2]-hardness of precedence constrained K-processor scheduling , 1995, Oper. Res. Lett..

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

[12]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.

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

[14]  Michael R. Fellows,et al.  Cutting Up is Hard to Do: the Parameterized Complexity of k-Cut and Related Problems , 2003, CATS.

[15]  Tony R. Martinez,et al.  The minimum feature set problem , 1994, Neural Networks.

[16]  Iyad A. Kanj,et al.  Tight lower bounds for certain parameterized NP-hard problems , 2004, Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004..

[17]  Jianer Chen.  Characterizing Parallel Hierarchies by Reducibilities , 1991, Inf. Process. Lett..

[18]  Giorgio Gambosi,et al.  Complexity and approximation: combinatorial optimization problems and their approximability properties , 1999 .

[19]  Martin Grohe,et al.  The parameterized complexity of database queries , 2001, PODS '01.

[20]  Mihalis Yannakakis,et al.  On Limited Nondeterminism and the Complexity of the V-C Dimension , 1996, J. Comput. Syst. Sci..

[21]  Krzysztof Pietrzak,et al.  On the parameterized complexity of the fixed alphabet shortest common supersequence and longest common subsequence problems , 2003, J. Comput. Syst. Sci..

[22]  Weijia Jia,et al.  Vertex Cover: Further Observations and Further Improvements , 2001, J. Algorithms.

[23]  Weijia Jia,et al.  Vertex Cover: Further Observations and Further Improvements , 1999, J. Algorithms.

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

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

[26]  Xiuzhen Huang,et al.  Parameterized complexity and polynomial-time approximation schemes , 2004 .

[27]  Ge Xia,et al.  Linear FPT reductions and computational lower bounds , 2004, STOC '04.

[28]  Liming Cai,et al.  On Fixed-Parameter Tractability and Approximability of NP Optimization Problems , 1997, J. Comput. Syst. Sci..