On parameterized intractability: Hardness and completeness

Computer Journal

Volumn 51, Issue 1, 2008, Pages 39-59

  Chen, Jianer ^a   Meng, Jie ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Exact algorithm; Fixed parameter tractability; Lower bound; Parameterized computation; W hierarchy

Indexed keywords

ALGORITHMS; COMPUTATION THEORY;

EXACT ALGORITHM; FIXED PARAMETER TRACTABILITY; LOWER BOUND; PARAMETERIZED COMPUTATION; W-HIERARCHY;

COMPUTATIONAL COMPLEXITY;

EID: 38349057717     PISSN: 00104620     EISSN: 14602067     Source Type: Journal    
DOI: 10.1093/comjnl/bxm036     Document Type: Article

References (77)

1. Garey, M.R. and Johnson, D.S. (1979) Computers and Intractability: A Guide to the Theory of NP- Completeness. Freeman, W. H. and Company, New York.
2. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A. and Protasi, M. (1999) Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties. Springer, Berlin, Heidelberg.
3. Motwani, R. and Raghavan, P. (1995) Randomized Algorithms. Cambridge University Press, New York.
4. Michalewicz, Z. and Fogel, D. (2000) How to Solve It: Modern Heuristics. Springer, Berlin.
5. Chen, J. and Kanj, I.A. (2003) Constrained minimum vertex cover in bipartite graphs: Complexity and parameterized algorithms. J. Comput. Syst. Sci., 67, 833-847.
6. Lichtenstein, O. and Pnueli, A. (1985) Checking that finite state concurrent programs satisfy their linear specification. Proc. 12th ACM Symp. Principles of Prog. Languages, pp. 97 -107.
7. Henglein, F. and Mairson, H.G. (1994) The complexity of type inference for higher-order typed lambda calculi. J. Funct. Program., 4 435-477.
8. Coppersmith, D. and Winograd, S. (1990) Matrix multiplication via arithmetic progression. J. Symb. Log., 9, 251-280.
9. Papadimitriou, C.H. and Yannakakis, M. (1999) On the complexity of database queries. J. Comput. Syst. Sci., 58, 407-427.
10. Downey, R. and Fellows, M. (1999) Parameterized Complexity. Springer-Verlag, Berlin.
11. Papadimitriou, C. (1994) Computational Complexity. Addison-Wesley, New York.
12. Cesati, M. Compendium of parameterized problems (2006 version). http:/Bravo.ce.uniroma2.it/home/cesati/research/compendium/.
13. Downey, R. and Fellows, M. (1995) Fixed-parameter tractability and completeness I: Basic results. SIAM J. Comput., 24, 873-921.
14. Downey, R. and Fellows, M. (1995) Fixed-parameter tractability and completeness II: On completeness for W[1]. Theor. Comput. Sci., 141, 109-131.
15. DIMACS Workshop on Faster Exact Algorithms for NP-Hard Problems, Princeton, NJ (2000).
16. Papadimitriou, C.H. and Yannakakis, M. (1991) Optimization, approximation, and complexity classes. J. Comput. Syst. Sci., 43, 425-440.
17. Impagliazzo, R. and Paturi, R. (2001) Which problems have strongly exponential complexity? J. Comput. Syst. Sci., 63, 512-530.
18. Abrahamson, K., Downey, R. and Fellows, M. (1995) Fixed-parameter tractability and completeness IV: On completeness of WP and PSPACE analogs. Ann. Pure Appl. Logic, 73, 235-276.
19. Woeginger, G. Exact algorithms for NP-hard problems: A survey. Proc. 5th Int. Workshop Combinatorial Optimization. Lecture Notes in Computer Science, Vol. 2570, pp. 185-207.
20. Chen, J., Huang, X., Kanj, I.A. and Xia, G. (2006) Strong computational lower bounds via parameterized complexity. J. Comput. Syst. Sci., 72, 1346-1367.
21. Buss, J. and Goldsmith, J. (1993) Nondeterminism within P. SIAM J. Comput., 22, 560-572.
22. Chen, J., Kanj, I.A. and Jia, W. (2001) Vertex cover: Further observations and further improvements. J. Algorithms, 41, 280-301.
23. Jones, N. and Pevzner, P. (2004) An Introduction to Bioinformatics Algorithms. The MIT Press, Cambridge, MA.
24. Bodlaender, H., Downey, R., Fellows, M., Hallett, M. and Wareham, H. (1995) Parameterized complexity analysis in computational biology. Comput. Appl. Biosci., 11, 49-57.
25. Deng, X., Li, G., Li, Z., Ma, B. and Wang, L. (2003) Genetic design of drugs without side-effects. SIAM J. Comput., 32, 1073-1090.
26. Gramm, J., Guo, J. and Niedermeier, R. (2006) Parameterized intractability of distinguishing substring selection. Theory Comput. Syst., 39, 545-560.
27. Chen, J., Chor, B., Fellows, M., Huang, X., Juedes, D., Kanj, I. and Xia, G. (2005) Tight lower bounds for certain parameterized NP-hard problems. Inf. Comput., 201, 216-231.
28. Chen, J., Huang, X., Kanj, I. and Xia, G. (2006) On the computational hardness based on linear FPT-reductions. J. Comb. Optim., 11 231-247.
29. Cai, L. and Juedes, D. (2003) On the existence of subexponential parameterized algorithms. J. Comput. Syst. Sci., 67, 789-807.
30. Alber, J., Bodlaender, H.L., Fernau, H., Kloks, T. and Niedermeier, R. (2002) Fixed parameter algorithms for dominating set and related problems on planar graphs. Algorithmica, 33, 461-493.
31. Fomin, F. and Thilikos, D. (2003) Dominating sets in planar graphs: branch-width and exponential speed-up. Proc. 14th Ann. ACM-SIAM Symp. Discrete Algorithms (SODA'03), pp. 168-177.
32. Cai, L. and Chen, J. (1997) On fixed-parameter tractability and approximability of NP optimization problems. J. Comput. Syst. Sci. 54, 465-474.
33. Chen, J., Huang, X., Kanj, I. and Xia, G. (2007) Polynomial time approximation schemes and parameterized complexity. Discret. Appl. Math., 155 180-193.
34. Kolaitis, P. and Thakur, M. (1995) Approximation properties of NP minimization classes. J. Comput. Syst. Sci., 50, 391-411.
35. Downey, R. (2003) Parameterized complexity for the skeptic. Proc. 18th Annual IEEE Conf. Computational Complexity, pp. 147-169.
36. Cesati, M. and Trevisan, L. (1997) On the efficiency of polynomial time approximation schemes. Inf. Process. Lett., 64, 165-171.
37. Bazgan, C. (1995) Schémas d'approximation et complexité paramétrée. Rapport de stage de DEA d'Informatique à Orsay
38. Flum, J. and Grohe, M. (2006) Parameterized Complexity Theory. Springer, New York.
39. Frick, M. and Grohe, M. (2001) Deciding first-order properties of locally tree-decomposable structures. J. ACM, 48, 1184-1206.
40. Downey, R., Fellows, M. and Regan, K. (1998) Parameterized circuit complexity and the W-hierarchy. Theor. Comput. Sci., 191 97-115.
41. Abrahamson, K., Ellis, J., Fellows, M. and Mara, M. (1989) On the complexity of fixed-parameter problems. Proc. 30th Annual IEEE Symp. Foundation of Computer Science, pp. 210-215.
42. k) time. J. ACM, 31, 361-376.
43. Cai, L., Chen, J., Downey, R. and Fellows, M. (1997) On the parameterized complexity of short computation and factorization. Arc. Math. Log., 36, 321-337.
44. Chandra, Kozen and Stockmeyer. (1981) Alternation. J. ACM, 28 114-133.
45. Flum, J. and Grohe, M. (2001) Fixed-parameter tractability, definability, and model-checking. SIAM J. Comput., 31, 113-145.
46. Downey, R., Fellows, M. and Regan, K. (1998) Descriptive Complexity and the W-Hierarchy. In Beame, P. and Buss, S. (eds), Proof Complexity and Feasible Arithmetics 39, AMS-DIMACS Volume Series, pp. 119-134.
47. Flum, J. and Grohe, M. (2005) Model-checking problems as a basis for parameterized intractability. Log. Methods Comput. Sci., 1(1:2 1-35.
48. Gu, J., Purdom, P., Franco, J. and Wah, B. (1997) Algorithms for the satisfiability (SAT) problem: A survey. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, AMS.
49. Schoning, U. (1999) A probabilistic algorithm for k-SAT and constraint satisfiability problems. Proc. 40th Annual IEEE Symp. Foundations of Computer Science (FOCS 1999), pp. 410-414.
50. Håstad, J. (1986) Computational Limitations for Small-Depth Circuits. The MIT Press, Cambridge, MA.
51. Cai, L. and Chen, J. (1995) On input read-modes of alternating Turing machines. Theor. Comput. Sci., 148, 33-55.
52. Cai, L. and Chen, J. (1997) On the amount of nondeterminism and the power of verifying. SIAM J. Comput., 26 733-750.
53. Cormen, T., Leiserson, C., Rivest, R. and Stein, C. (2001) Introduction to Algorithms (2nd ed). McGraw-Hill Book Company, Boston, MA.
54. Papadimitriou, C.H. and Yannakakis, M. (1996) On limited nondeterminism and the complexity of VC dimension. J. Comput. Syst. Sci., 53 161-170.
55. Kintala, C. and Fisher, P. (1980) Refining nondeterminism in relativized polynomial-time bounded computations. SIAM J. Comput., 9, 46-53.
56. Cai, L., Chen, J., Downey, R. and Fellows, M. (1995) On the structure of parameterized problems in NP. Inf. Comput., 123, 38-49.
57. Cai, L. (1994) Nondeterminism and Optimization. PhD Dissertation, Department of Computer Science, Texas A&M University, College Station, TX, USA.
58. Muller-Olm, M., Schmidt, D. and Steffen, B. (1999) Model-checking: A tutorial introduction, Lecture Notes in Computer Science 1694 (SAS'99), pp. 330-354.
59. Downey, R., Estivill-Castro, V., Fellows, M., Prieto-Rodriguez, E. and Rosamond, F. (2003) Cutting up is hard to do: The parameterized complexity of k-cut and related problems. Electron. Notes Theor. Comput. Sci., 78, 205-218.
60. Flum, J. and Grohe, M. (2004) Parameterized complexity and subexponential time. Bull. EATCS, 84, 71-100.
61. Frick, M. and Grohe, M. (2004) The complexity of first-order and monadic second-order logic revisited. Ann. Pure Appl. Log., 130, 3-31.
62. 2 n nondeterministic bits. J. Comput. Syst. Sci., 72, 34-71.
63. poly(k). Lecture Notes in Computer Science 3162 (IWPEC 2004), pp. 49-60.
64. Cesati, M. (2003) The Turing way to parameterized complexity. J. Comput. Syst. Sci., 67, 654-685.
65. Chen, Y. and Flum, J. (2003) Machine characterizations of the classes of the W-hierarchy. Lecture Notes in Computer Science 2803 (CSL'03), pp. 114-127.
66. Chen, Y., Flum, J. and Grohe, M. (2003) Bounded nondeterminism and alternation in parameterized complexity theory. Proc. 18th Annual IEEE Conf. Computational Complexity, pp. 13-29.
67. Buss, J. and Islam, T. (2006) Simplifying the weft hierarchy. Theor. Comput. Sci., 351, 303-313.
68. Buss, J. and Islam, T. Algorithms in the W-hierarchy. Theory Comput. Syst., to appear.
69. Valiant, L. (1979) The complexity of computing the permanent. Theor. Comput. Sci., 8, 189-201.
70. Flum, J. and Grohe, M. (2004) The parameterized complexity of counting problems. SIAM J. Comput., 33, 892-922.
71. Alon, N., Yuster, R. and Zwick, U. (1995) Color-coding. J. ACM, 42, 844-856.
72. McCartin, C. (2006) Parameterized counting problems. Ann. Pure Appl. Log., 138, 147-182.
73. Damaschke, P. (2006) Parameterized enumeration, transversals, and imperfect phylogeny reconstruction. Theor. Comput. Sci., 351 337-350.
74. Fernau, H. (2002) On parameterized enumeration. Proc. 8th Annual Int. Conf. Computing and Combinatorics (CoCoon 2002), Lecture Notes in Computer Science, Vol. 2383, pp. 564-573.
75. Gramm, J. and Niedermeier, R. (2003) A fixed-parameter algorithm for minimum quartet inconsistency. J. Comput. Syst. Sci., 67, 723-741.
76. Chen, J., Kanj, I., Meng, J., Xia, G. and Zhang, F. (2006) On the effective enumerability of NP problems. Proc. 2nd Int. Workshop on Parameterized and Exact Computations (IWPEC 2006), Lecture Notes in Computer Science, Vol. 4169, pp. 215-226.
77. Grohe, M. (2001) Generalized model-checking problems for first-order logic. Proc. 18th Annual Symp. Theoretical Aspects of Computer Science (STACS'01), pp. 12-26.