On weighted vs unweighted versions of combinatorial optimization problems

Information and Computation

Volumn 167, Issue 1, 2001, Pages 10-26

  Crescenzi, Pierluigi ^a   Silvestri, Riccardo ^b   Trevisan, Luca ^c  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

^c Department of Earth and Environmental Sciences   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; SET THEORY;

DISJOINT SETS;

COMPUTATIONAL COMPLEXITY;

EID: 0035947797     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1006/inco.2000.3011     Document Type: Conference Paper

References (34)

1. Alimonti, P. (1995), Non-oblivious local search for graphs and hypergraphs coloring problems, in "Proc. 21st Workshop on Graph-Theoretic Concepts in Computer Science," LNCS 1017, pp. 167-180. Springer-Verlag, Berlin.
2. Alon, N., and Spencer, J. (1992), "The Probabilistic Method." Wiley Interscience, New York.
3. Arora, S., Lund, C., Motwani, R., Sudan, M., and Szegedy, M. (1992), Proof verification and hardness of approximation problems, in "Proc. 33rd IEEE Symposium on Foundations of Computer Science," pp. 14-23.
4. Arora, S., and Safra, S. (1992), Probabilistic checking of proofs: A new characterization of NP, in "Proc. 33rd IEEE Symposium on Foundations of Computer Science," pp. 2-13.
5. Bellare, M., Goldreich, O., and Sudan, M. (1998), Free bits, PCP's and non-approximability, SIAM J. Comput. 27, 804-915.
6. Bellare, M., Goldwasser, S., Lund, C., and Russell, A. (1993), Efficient probabilistically checkable proofs and applications to approximation, in "Proc. 25th ACM Symposium on Theory of Computing," pp. 294-304.
7. Bellare, M., and Sudan, M. (1994), Improved non-approximability results, in "Proc. 26th ACM Symposium on Theory of Computing," pp. 184-193.
8. Boppana, R., and Halldórsson, M. M. (1992), Approximating maximum independent sets by excluding subgraphs, Bit 32, 180-196.
9. Bovet, D. P., and Crescenzi, P. (1994), "Introduction to the Theory of Complexity," Prentice Hall, New York.
10. Crescenzi, P., and Kann, V., A compendium of NP optimization problems, latest version available on-line at http://www.nada.kth.se/̃viggo/problemlist/compendium.html.
11. Crescenzi, P., Kann, V., Silvestri, R., and Trevisan, L., Structure in approximation classes, in "Proc. 1st Computing and Combinatorics Conference," LNCS 959, pp. 539-548, Springer-Verlag, Berlin
12. Crescenzi, P., and Trevisan, L. (1994). On approximation scheme preserving reducibility and its applications, in "Proc. 14th Conference on Foundations of Software Technology and Theoretical Computer Science," LNCS 880, pp. 330-341, Springer-Verlag, Berlin.
13. Davenport, H. (1980), "Multiplicative Number Theory," 2nd ed., Springer-Verlag, Berlin.
14. Feige, U., Goldwasser, S., Lovasz, L., Safra, S., and Szegedy, M. (1996), Interactive proofs and the hardness of approximating cliques, J. Assoc. Comput. Mach. 43(2), 268-292.
15. Feige, U., and Kilian, J. (1994), Two prover protocols Low error at affordable rates, in "Proc. ACM 26th Symposium on Theory of Computing," pp. 172-183.
16. Garey, M. R., and Johnson, D. S. (1978), Strong NP-completeness results: Motivation, examples, and implications. J. Assoc. Comput. Mach. 25, 499-508.
17. Garey, M. R., and Johnson, D. S. (1979), "Computers and Intractability: A Guide to the Theory of NP-Completeness," Freeman, New York.
18. Gavril, F., Cited in [17, p. 134].
19. Goldreich, O., and Wigderson, A. (1994), Tiny families of mixing functions, in "Proc. 26th ACM Symposium on Theory of Computing," pp. 574-583.
20. Halldórsson, M. M. (1995), Approximations via partitioning, Technical Report IS-RR-95-0003F, JAIST, March.
21. Håstad, J. (1996), Testing the long code and hardness for clique, in "Proc. 28th ACM Symposium on Theory of Computing," pp. 11-19.
22. 1-ε, in "Proc. 37th IEEE Symposium on Foundations of Computer Science," pp. 627-636.
23. Håstad, J. (1997), Some optimal inapproximability results, in "Proc. 29th ACM Symposium on Theory of Computing," pp. 1-10.
24. Ibarra, O. H., and Kim, C. E. (1975), Fast approximation for the knapsack and sum of subset problems, J. Assoc. Comput. Mach. 22, 463-468.
25. Kann, V., Khanna, S., Lagergren, J., and Panconesi, A. (1997), On the hardness of approximating Max k-Cut and its dual, Chicago J. Theoret. Comput. Sci. 2.
26. Kann, V., Lagergren, J., and Panconesi, A. (1996), Approximability of maximum splitting of k-sets and some other APX-complete problems, Inform. Process. Lett. 58, 105-110.
27. Khanna, S., Motwani, R., Sudan, M., and Vazirani, U. (1994), On syntactic versus computational views of approximability, in "Proc. 35th IEEE Symposium on Foundations of Computer Science," pp. 819-830.
28. Lubotzky, A., Phillips, R., and Sarnak, P. (1988), Ramanujan graphs, Combinatorica 8(3), 261-277.
29. Marathe, M. V., and Ravi, S. S. (1996), On approximation algorithms for the minimum satisfiability problem, Inform. Process. Lett. 58(1), 23-29.
30. Nemhauser, G. L., and Trotter, L. E. (1975), Vertex packing: Structural properties and algorithms, Math. Programming 8, 232-248.
31. Papadimitriou, C. H., and Yannakakis, M. (1991), Optimization, approximation, and complexity classes, J. Comput. System Sci. 43, 425-440.
32. Trevisan, L., Sorkin, G., Sudan, M., and Williamson, D. P. (1996), Gadgets, approximation, and linear programming, in "Proc. 37th IEEE Symposium on Foundations of Computer Science," pp. 617-626.
33. Yannakakis, M. (1994), On the approximation of maximum satisfiability, J. Algorithms 17, 475-502.
34. Zimand, M. (1995), Weighted NP optimization problems: Logical definability and approximation properties, in "Proc. 10th IEEE Conference on Structure in Complexity Theory," pp. 12-28.