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4. Bibliography
G. Ausiello, A. D'Atri and M. Protasi, “Structure preserving reductions among convex optimization problems,” J Comput and System Sci, 21 (1980), 136–153; (first appeared in Proc 4th ICALP, Lecture Notes in Computer Science, 52 (1977), 45–60.)
L. Berman and J. Hartmanis, “On isomorphism and density of NP and other complete sets,” SIAM J Comput, 1 (1977), 305–322.
A. Bertoni, D. Bruschi, D. Joseph, M. Sitharam and P. Young, “Generalized Boolean hierarchies and Boolean hierarchies over RP,” Univ Wisconsin CS Dept Tech Report, #809, 1–40; (short abstract to appear in FCT '89 Proceedings.)
J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, “The Boolean hierarchy II: applications,” SIAM J Comput, 7 (1989), 95–111.
P. Crescenzi and A. Panconesi, “Completeness in approximation classes,” to appear in FCT '89 Proceedings, (1989), 16 pages.
R. Fagin, “Generalized first-order spectra, and polynomial-time recognizable sets,” Complexity and Computations, R. Karp (ed.), AMS, (1974).
M. Garey and D. Johnson, “Computers and Intractability: A Guide to the Theory of NP-Completeness,” Freeman, 1979.
T. Gonzales and S. Sahni, “P-complete approximation problems,” J ACM, 23 (1976), 555–565.
B. Hodgson and C. Kent, “An arithmetical characterization of NP,” Theor Comput Sci, 21 (1982), 255–267.
D. Hochbaum and D. Shmoys, “A unified approach to approximation algorithms for bottleneck problems,” J ACM, 33 (1986), 533–550.
O. Ibarra and C. Kim, “Fast approximation algorithms for the knapsack and sum of subsets problems,” J ACM, 22 (1975), 463–468.
D. Johnson, C. Aragon, L. McGeoch, and C. Schevon, “Optimization by simulated annealing: an experimental evaluation,” Operations Research, to appear.
D. Johnson, “Approximation algorithms for combinatorial problems,” J Comput and System Sci, 9 (1974), 256–278.
D. Johnson, C. Papadimitriou and M. Yannakakis, “How easy is local search?,” J Comput and System Sci, 37 (1988), 79–100; (first appeared in Proc 26th IEEE Symp Foundations of Comput Sci, (1985), 39–42.)
D. Joseph and P. Young, “Some remarks on witness functions for polynomial reducibilities in NP,” Theor Comput Sci, 39 (1985), 225–237.
N. Karmakar and R. Karp, “An efficient approximation scheme for the one-dimensional bin-packing problem,” IEEE 23rd Symp Foundations of Comput Sci, (1982), 312–320.
S. Kirkpatrick, C. Gelat, and M. Vecchi, “Optimization by simulated annealing,” Science, 220 (1983), 671–680.
M. Krentel, “The complexity of optimization problem,” J Comput and System Sci, 36 (1988), 490–509; (first appeared in Proc 18th ACM Symp Theory on Comput, (1986), 69–76.)
M. Krentel, “On finding locally optimal solutions,” Proc Structure in Complexity Conference, (1989), 132–137.
E. Leggett and J. Moore, “Optimization problems and the polynomial time hierarchy,” Theor Comput Sci, 15 (1981), 279–289.
N. Lynch and R. Lipton “On structure preserving reductions,” Siam J Comput, 7 (1978), 119–126.
P. Orponen and H. Mannila, “On approximation preserving reductions: complete problems and robust measures,” Tech Report, University of Helsinki, 1987.
R. Nigmatullin, “Complexity of the approximate solution of combinatorial problems”, Dokl Akad Nauk, SSSR 224, (1975) 289–292 (in Russian), English translation in Soviet Math Dokl, 16, 1199–1203.
C. Papadimitriou, “On the complexity of unique solutions”, J ACM, 31 (1984), 392–400.
A. Paz and S. Moran, “Non deterministic polynomial optimization problems and their approximation,” Theor Comput Sci, 15 (1981), 251–277; (first appeared in Proc 4th ICALP, Lecture Notes in Computer Science, 52 (1977), 45–60.)
C. Papadimitriou and D. Wolfe, “The complexity of facets resolved,” J Comput and System Sci, 37 (1988), 2–13; (first appeared in Proc IEEE 26th Symp on Foundations of Comput Sci, (1985), 74–78).
C. Papadimitriou and M. Yannakakis, “The complexity of facets (and some facets of complexity),” J Computer and System Sciences, 28 (1984), 244–259, (first appeared in Proc 14th ACM Symp Theory of Comput, (1982), 255–260.)
C. Papadimitriou and M. Yannakakis, “Optimization, approximation, and complexity classes,” Proc 20th ACM Symp Theory Comput, (1988), 229–234.
S. Sahni, “Algorithms for scheduling independent tasks,” J ACM, 23 (1976), 116–127.
K. Wagner, “More complicated questions about maxima and minima, and some closure properties of NP,” Theor Comput Sci, 51 (1987), 53–80; (first appeared in Proc 13th ICALP, Lecture Notes Computer Science, 226 (1986), 434–443.)
K. Wagner, “Bounded query computations,” Proc Structure in Complexity Conference, (1988), 260–277.
K. Wagner and G. Wechsung, “Computational complexity,” D. Reidel Publishing, 1986.
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Bruschi, D., Joseph, D., Young, P. (1989). A structural overview of NP optimization problems. In: Djidjev, H. (eds) Optimal Algorithms. OA 1989. Lecture Notes in Computer Science, vol 401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51859-2_17
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DOI: https://doi.org/10.1007/3-540-51859-2_17
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