Monotonic reductions, representative equivalence, and compilation of intractable problems

Journal of the ACM

Volumn 48, Issue 6, 2001, Pages 1091-1125

  Liberatore, Paolo ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Compilability; Preprocessing

Indexed keywords

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; COMPUTER SCIENCE; DATA STRUCTURES; GEOMETRY; MATRIX ALGEBRA; PROGRAM COMPILERS;

COMPILABILITY; MONOTONIC REDUCTIONS; PREPROCESSING; RESEARCHERS;

PROBLEM SOLVING;

EID: 0000579854     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/504794.504795     Document Type: Article

References (52)

1. AGARWAL, P., ARGE, L., ERICKSON, J., FRANCIOSA, P., AND VITTER, S. 2000. Efficient searching with linear constraints. J. Comput. Syst. Sci. 61, 2, 194-216.
2. ALLEMANG, D., TANNER, M. C., BYLANDER, T., AND JOSEPHSON, J. R. 1987. Computational complexity of hypothesis assembly. In Proceedings of the 10th International Joint Conference on Artificial Intelligence. Morgan-Kaufmann, San Mateo, Calif., pp. 1112-1117.
3. ARYA, S., MOUNT, D., NETANYAHU, N., SILVERMAN, R., AND WU, A. 1998. An optimal algorithm for approximate nearest neighbor searching fixed dimensions. J. ACM 45, 6, 891-923.
4. BEIMEL, A., ISHAI, Y., AND MALKIN, T. 2000. Reducing the server computation in private information retrieval: PIR with preprocessing, In Proceedings of Advances in Cryptography (CRYPTO'2000). Springer-Verlag, Berlin, Germany, pp. 55-73.
5. BOUTILIER, C. 1993. Revision sequences and nested conditionals. In Proceedings of the 13th International Joint Conference on Artificial Intelligence. Morgan-Kaufmann, San Mateo, Calif., pp. 519-525.
6. BYLANDER, T. 1991. Complexity results for planning. In Proceedings of the 12th International Joint Conference on Artificial Intelligence. Morgan-Kaufmann, San Mateo, Calif., pp. 274-279.
7. BYLANDER, T., ALLEMANG, D., TANNER, M. C., AND JOSEPHSON, J. R. 1991. The computational complexity of abduction. Artif. Int. 49, 25-60.
8. CADOLI, M., AND DONINI, F. M. 1997. A survey on knowledge compilation. AI Communi. 10, 137-150.
9. CADOLI, M., DONINI, F. M., LIBERATORE, P., AND SCHAERF, M. 1995. The size of a revised knowledge base. In Proceedings of the 14th ACM Symposium on Principles of Database Systems. ACM, New York, pp. 151-162.
10. CADOLI, M., DONINI, F., LIBERATORE, P., AND SCHAERF, M. 1996. Comparing space efficiency of prepositional knowledge representation formalisms. In Proceedings of the 5th International Conference on the Principles of Knowledge Representation and Reasoning. Morgan-Kaufmann, San Mateo, Calif., pp. 364-373.
11. CADOLI, M., DONINI, F. M., LIBERATORE, P., AND SCHAERF, M. 2001. Preprocessing of intractable problems. Inf. Comput. to appear.
12. CADOLI, M., DONINI, F. M., SCHAERF, M., AND SILVESTRI, R. 1997. On compact representations of propositional circumscription. Theoret. Comput. Sci. 182, 183-202.
13. CAI, L., CHEN, J., DOWNEY, R., AND FELLOWS, M. 1995. On the structure of parameterized problems in NP. Inf. Comput. 123, 1, 38-49.
14. CAI, L., CHEN, J., DOWNEY, R., AND FELLOWS, M. 1997. Advice classes of parameterized tractability. Ann. Pure Appl. Logic 84, 119-138.
15. CHANDRA, A., AND MERLIN, P. 1977. Optimal implementation of conjunctive queries in relational data bases. In Proceedings of the 9th ACM Symposium on Theory of Computing. ACM, New York, pp. 77-90.
16. CONSOLE, L., PORTINALE, L., AND THESEIDER DUPRÉ, D. 1996. Using compiled knowledge to guide and focus abductive diagnosis. IEEE Tran. Knowl. Data Eng. 8, 5, 690-706.
17. DECHTER, R. 1998. Constraint satisfaction. In. MIT Encyclopedia of the Cognitive Sciences. Vol. Computational Intelligence. The MIT Press, Cambridge, Chap. 16, Mass, pp. 195-197.
18. DOWNEY, R. G., AND FELLOWS, M. F. 1999. Parameterized Complexity. Springer-Verlag, Berlin, Germany
19. EITER, T., AND GOTTLOB, G. 1995. The complexity of logic-based abduction. J. ACM 42, 1, 3-42.
20. FIKES, R., AND NlLSSON, N. 1971. STRIPS: A new approach to the application of theorem proving to problem solving. Artif. Int. 2, 189-208.
21. GALIL, Z. 1995. A constant-time optimal parallel string-matching algorithm. J. ACM 42, 4, 908-918.
22. GAREY, M. R., AND JOHNSON, D. S. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, San Francisco, Calif.
23. GELFOND, M., AND LIFSCHITZ, V. 1993. Representing action and change by logic programs. J. Logic Prog. 17, 301-322.
24. GOGIC, G., KAUTZ, H. A., PAPADIMITRIOU, C., AND SELMAN, B. 1995. The comparative linguistics of knowledge representation. In Proceedings of the 14th International Joint Conference on Artificial Intelligence. Morgan-Kaufmann, San Mateo, Calif., pp. 862-869.
25. GOHBERG, I., AND OLSHEVSKY, V. 1994. Fast algorithms with preprocessing for matrix-vector multiplication problems. J. Complex. 10, 4, 411-427.
26. GOTTLOB, G., LEONE, N., AND SCARCELLO, F. 1998. The complexity of acyclic conjunctive queries. In Proceedings of the 39th Annual Symposium on the Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., pp. 706-715.
27. JANSEN, K., AND MÜLLER, H. 1995. The minimum broadcast time problem for several processor networks. Theoret. Comput. Sci. 147, 69-85.
28. JOHNSON, D. S. 1990. A catalog of complexity classes. In Handbook of Theoretical Computer Science, Vol. A. J. van Leeuwen, Ed. Elsevier Science Publishers, Amsterdam, The Netherlands, Chapter 2, pp. 67-161.
29. KARP, R. 1972. Reducibility among combinatorial problems. In Complexity of Computer Computations. R. Miller and J. Thatcher, Eds. Plenum Press, New York, pp. 85-103.
30. KARP, R. 1975. On the computational complexity of combinatorial problems. Network 5, 45-70.
31. KARP, R. M., AND LIPTON, R. J. 1980. Some connections between non-uniform and uniform complexity classes. In Proceedings of the 12th ACM Symposium on Theory of Computing. ACM, New York, pp. 302-309.
32. KAUTZ, H. A., AND SELMAN, B. 1992. Forming concepts for fast inference. In Proceedings of the 10th National Conference on Artificial Intelligence. AAAI/MIT Press, Menlo Park, Calif., pp. 786-793.
33. KAVRAKI, L., LATOMBE, J.-C., MOTWANI, R., AND RAGHAVAN, P. 1998. Randomized query processing in robot path planning. J. Comput. Syst. Sci. 57, 1, 50-60.
34. LIBERATORE, P. 1997a. The complexity of iterated belief revision. In Proceedings of the 6th International Conference on Database Theory. Springer-Verlag, Berlin, Germany, pp. 276-290.
35. LIBERATORE, P. 1997b. The complexity of the language A. Electron. Trans. Artif. Int. 1, 1-3, 13-37.
36. LIBERATORE, P. 1998a. Compilation of intractable problems and its application to Artificial Intelligence. Ph.D. dissertation, Dipartimento di Informatica e Sistemistica, Università di Roma "La Sapienza," Rome, Italy.
37. LIBERATORE, P. 1998b. On the compilability of diagnosis, planning, reasoning about actions, belief revision, etc. In Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning. Morgan-Kaufmann, San Mateo, Calif., pp. 144-155.
38. LIBERATORE, P. 1999. Monotonic reductions, representative equivalence, and compilation of intractable problems. Tech. Rep. 30-99, Dipartimento di Informatica e Sistemistica, Università di Roma "La Sapienza," Rome, Italy.
39. LIBERATORE, P., AND SCHAERF, M. 2000. Compilability of abduction. In Proceedings of the 17th National Conference on Artificial Intelligence. AAAI/MIT Press, Menlo Park, Calif., pp. 349-354.
40. MCILRAITH, S. 1998. Logic-based abductive inference. Tech. Rep. 19-98, Knowledge Systems Laboratory, Stanford University, Stanford, Calif.
41. NAYAK, A., 1994. Iterated belief change based on epistemic entrenchment. Erkenntnis 41, 353-390.
42. NAYAK, A., AND FOO, N. 1998. Reasoning without minimality. In Proceedings of the 5th Pacific Rim Conference on Artificial Intelligence. Springer-Verlag, Berlin, Germany, pp. 122-133.
43. NTAFOS, S., AND HAKIMI, S. 1979. On path cover problems in digraphs and applications to program testing. IEEE Tran. Softw. Eng. SE-5, 520-529.
44. PENG, Y., AND REGGIA, J. 1986. Plausibility of diagnostic hypothesis. In Proceedings of the 5th National Conference on Artificial Intelligence. AAAI/MIT Press, Menlo Park, Calif., pp., 140-145.
45. RAO, S. V. N. 1993. Computational complexity issues in operative diagnosis of graph-based sytems. IEEE Trans. Comput. 42, 4, 447-457.
46. SELMAN, B., AND KAUTZ, H. A. 1996. Knowledge compilation and theory approximation. J. ACM 43, 193-224.
47. SELMAN, B., AND LEVESQUE, H. J. 1990. Abductive and default reasoning: A computational core. In Proceedings of the 8th National Conference on Artificial Intelligence. AAAI/MIT Press, Menlo Park, Calif., pp. 343-348.
48. SPOHN, W. 1988. Ordinal conditional functions: A dynamic theory of epistemic states. In Causation in Decision, Belief Change, and Statistics. Kluwer Academics, Dordrecht, The Netherlands, pp. 105-134.
49. TADEPALLI, P., AND NATARAJAN, B. 1996. A formal framework for speedup learning from problems and solutions. J. Artif. Int. Res. 4, 445-475.
50. VAN BEEK, P., AND DECHTER, R. 1997. Constraint tightness and looseness versus local and global consistency. J. ACM 44, 4, 549-566.
51. VENKATESAN, S., AND RAMARAO, K. 1994. Computing associative functions distributively in spite of link failures. J. Parall. Distr. Comput. 23, 3, 399-410.
52. WILLIAMS, M. 1994. Transmutations of knowledge systems. In Proceedings of the 4th International Conference on the Principles of Knowledge Representation and Reasoning. Morgan-Kaufmann, San Mateo, Calif., pp. 619-629.