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N. Alon, L. Babai, and A. Itai (1986), “A fast and simple randomized parallel algorithm for the maximal independent set problem”, J. Algorithms 7, 567–583.
R. Anderson, and E.W. Mayr (1984), “A P-complete problem and approximation to it”, Technical Report STAN-CS-84-1014, Department of Computer Science, Stanford University.
A. Andreev, A. Clementi, P. Crescenzi, E. Dahlhaus, S. De Agostino, and J.D.P. Rolim (1995), “The parallel complexity of approximating the high degree subgraph problem”, Proc. 6th Annual International Symposium on Algorithms and Computation, to appear.
B.S. Baker (1994), “Approximation algorithms for NP-complete problems on planar graphs”, J. ACM 41, 153–180.
B. Berger, and J. Rompel (1989), “Simulating (logc n)-wise independence in NC”, Proc. 30th FOCS, 2–7.
B. Berger, J. Rompel, and P.W. Shor (1989), “Efficient NC algorithms for set cover with applications to learning and geometry”, Proc. 30th FOCS, 54–59.
G. Bongiovanni, P. Crescenzi, and S. De Agostino (1990), “Descriptive Complexity and Parallel Approximation of Optimization Problems”, unpublished manuscript (these results also appeared in P. Crescenzi, Descriptive complexity, average measure, and parallel approximation algorithms, Ph.D. Thesis, Department of Computer and Systems Science, University of Rome “La Sapienza”, 1991).
E. Cohen (1992), “Approximate max flow on small depth networks”, Proc. 33rd FOCS, 648–658.
P. Crescenzi, and V. Kann (1995), “A compendium of NP optimization problems”, Technical Report SI/RR — 95/01, Department of Computer Science, University of Rome “La Sapienza” (available by anonymous ftp either at encore.dsi.uniromal.it as /pub/crescenzi/compendium.ps.Z or at nada.kth.se as Theory/Viggo-Kann/compendium.ps.Z).
P. Crescenzi, V. Kann, R. Silvestri, and L. Trevisan (1995), “Structure in approximation classes”, Proc. 1st COCOON, to appear.
J. Diaz, M. J. Serna, and J. Toran (1993), “Parallel approximation schemes for problems on planar graphs”, Proc. 1st ESA, 145–154.
P. Erdos (1963), “On the structure of linear graphs”, Israel Journal of Mathematics 1, 156–160.
M.R. Garey, and D.S. Johnson (1979), Computers and intractability: a guide to the theory of NP-completeness. Freeman.
A. Goldberg, S. Plotkin, D. Shmoys, and E. Tardos (1992), “Interior point methods in parallel computation”, SIAM J. Computing 21, 140–150.
R. Greenlaw, H.J. Hoover, and W.L. Ruzzo (1995), Limits to parallel computation: P-completeness theory, Oxford University Press.
T.J. Harris (1994), “A survey of PRAM simulation techniques”, ACM Computing Surveys, 26, 187–206.
H.B. Hunt III, M.V. Marathe, V. Radhakrishnan, S.S. Ravi, D.J. Rosenkrantz, and R.E. Stearns (1993), “Every Problem in MAX SNP has a Parallel Approximation Algorithm”, manuscript.
H.B. Hunt III, M.V. Marathe, V. Radhakrishnan, S.S. Ravi, D.J. Rosenkrantz, and R.E. Stearns (1994), “Approximation schemes using L-reductions”, 14th FSTTCS, 342–353.
A. Joffe (1974), “On a set of almost deterministic k-independent random variables”, Ann. Probability 2, 161–162.
D.S. Johnson (1974), “Approximation algorithms for combinatorial problems”, J. Comput. System Sci. 9, 256–278.
R. Karp, and V. Ramachandran (1990), “Parallel algorithms for shared-memory machines”, in Handbook of Theoretical Computer Science: Algorithms and Complexity, J. van Leeuwen (ed.), Elsevier, 869–941.
R. Karp, and A. Wigderson (1985), “A fast parallel algorithm for the maximal independent set problem”, J. of ACM, 32, 762–773.
S. Khuller, U. Vishkin, and N. Young (1994), “Primal-dual parallel approximation technique applied to weighted set and vertex covers”, J. of Algorithms, 280–289.
L.M. Kirousis, M.J. Serna, and P. Spirakis (1989), “The parallel complexity of the connected subgraph problem”, Proc. 30th FOCS, 446–456.
L. Kucera (1982), “Parallel computation and conflicts in memory access”, Information Processing Letters, 14, 93–96.
M. Luby (1986), “A simple parallel algorithm for the maximal independent set Problem”, SIAM J. Computing 15, 1036–1053.
M. Luby (1988), “Removing randomness in parallel computation without a processor penalty”, Proc. 29th FOCS, 162–173.
M. Luby, and N. Nisan (1993), “A parallel approximation algorithm for positive linear programming”, Proc. 25th STOC, 448–457.
E.W. Mayr (1988), “Parallel approximation algorithms”, Proc. Fifth Generation Computer Systems, 542–551.
C.H. Papadimitriou, and K. Steiglitz (1982), Combinatorial optimization. Algorithms and complexity. Prentice-Hall.
C.H. Papadimitriou, and M. Yannakakis (1991), “Optimization, approximation, and complexity classes”, J. Comput. System Sci. 43, 425–440.
S. Rajagopalan, and V.V. Vazirani (1993), “Primal-dual RNC approximation algorithms for (multi)-set (multi)-cover and covering integer programs”, Proc. 34th FOCS, 322–331.
M. Serna, and P. Spirakis (1989), “The approximability of problems complete for P”, Proc. International Symposium on Optimal Algorithms, 193–204.
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© 1996 Springer-Verlag Berlin Heidelberg
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Bovet, D.P., Clementi, A., Crescenzi, P., Silvestri, R. (1996). Parallel approximation of optimization problems. In: Ferreira, A., Pardalos, P. (eds) Solving Combinatorial Optimization Problems in Parallel. Lecture Notes in Computer Science, vol 1054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027116
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