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Volumn 54, Issue 2, 1997, Pages 317-331

The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; NONLINEAR PROGRAMMING; PROBLEM SOLVING;

EID: 0031119485     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1997.1472     Document Type: Article
Times cited : (287)

References (45)
  • 2
    • 0029638653 scopus 로고    scopus 로고
    • The complexity and approximability of finding maximum feasible subsystems of linear relations
    • E. Amaldi and V. Kann, The complexity and approximability of finding maximum feasible subsystems of linear relations, Theoret. Comput. Sci. 147 (1995), 187-210; an earlier version is in Proceedings STACS, 1994.
    • (1995) Theoret. Comput. Sci. , vol.147 , pp. 187-210
    • Amaldi, E.1    Kann, V.2
  • 3
    • 0029638653 scopus 로고    scopus 로고
    • E. Amaldi and V. Kann, The complexity and approximability of finding maximum feasible subsystems of linear relations, Theoret. Comput. Sci. 147 (1995), 187-210; an earlier version is in Proceedings STACS, 1994.
    • Proceedings STACS, 1994
  • 4
    • 0347450265 scopus 로고
    • On the Approximability of Some NP-Hard Minimization Problems for Linear Systems
    • Cornell Computational Optimization Project, Cornell University, Ithaca, NY
    • E. Amaldi and V. Kann, "On the Approximability of Some NP-Hard Minimization Problems for Linear Systems," Technical Report 95-7, Cornell Computational Optimization Project, Cornell University, Ithaca, NY, 1995.
    • (1995) Technical Report 95-7
    • Amaldi, E.1    Kann, V.2
  • 9
    • 51249173801 scopus 로고
    • On Lovász's lattice reduction and the nearest lattice point problem
    • L. Babai, On Lovász's lattice reduction and the nearest lattice point problem, Combinatorica II (1986), 1-14.
    • (1986) Combinatorica , vol.2 , pp. 1-14
    • Babai, L.1
  • 11
    • 0002771903 scopus 로고
    • Non-deterministic exponential time has two-prover interactive protocols
    • L. Babai, L. Fortnow, and C. Lund, Non-deterministic exponential time has two-prover interactive protocols, Comput. Complexity 1 (1991), 16-25.
    • (1991) Comput. Complexity , vol.1 , pp. 16-25
    • Babai, L.1    Fortnow, L.2    Lund, C.3
  • 12
    • 0347117118 scopus 로고
    • Interactive Proofs and Approximations
    • M. Bellare, "Interactive Proofs and Approximations," IBM Res. Rep. RC 17969, 1992.
    • (1992) IBM Res. Rep. RC 17969
    • Bellare, M.1
  • 14
    • 0345581486 scopus 로고
    • The complexity of approximating non-linear programs
    • (P. M. Pardalos, Ed.), World Scientific, Singapore
    • M. Bellare and P. Rogaway, The complexity of approximating non-linear programs, in "Complexity of Numerical Optimization" (P. M. Pardalos, Ed.), World Scientific, Singapore, 1993; preliminary version, IBM Research Report RC 17831, March 1992.
    • (1993) Complexity of Numerical Optimization
    • Bellare, M.1    Rogaway, P.2
  • 15
    • 0346819561 scopus 로고
    • March
    • M. Bellare and P. Rogaway, The complexity of approximating non-linear programs, in "Complexity of Numerical Optimization" (P. M. Pardalos, Ed.), World Scientific, Singapore, 1993; preliminary version, IBM Research Report RC 17831, March 1992.
    • (1992) IBM Research Report RC 17831
  • 20
    • 0004142253 scopus 로고
    • Cambridge Univ. Press, Cambridge
    • B. Bollobás, "Combinatorics," Cambridge Univ. Press, Cambridge, 1986.
    • (1986) Combinatorics
    • Bollobás, B.1
  • 21
    • 0025403933 scopus 로고
    • The hardness of decoding linear codes with preprocessing
    • J. Bruck and M. Naor, The hardness of decoding linear codes with preprocessing, IEEE Trans. Inform. Theory (1990), 381-385.
    • (1990) IEEE Trans. Inform. Theory , pp. 381-385
    • Bruck, J.1    Naor, M.2
  • 22
    • 0348080435 scopus 로고
    • The complexity of the max-word problem and the power of one-way interactive proof systems
    • A. Condon, The complexity of the max-word problem and the power of one-way interactive proof systems, Comput. Complexity 3 (1993), 292-305; Preliminary version appeared in "Proc. 8th Symp. on Theor. Aspects of Comp. Sci.," Lect. Notes in Comput. Sci., Springer-Verlag, New York/Berlin, pp. 456-465, 1991.
    • (1993) Comput. Complexity , vol.3 , pp. 292-305
    • Condon, A.1
  • 23
    • 0348080435 scopus 로고
    • "Proc. 8th Symp. on Theor. Aspects of Comp. Sci.," Springer-Verlag, New York/Berlin
    • A. Condon, The complexity of the max-word problem and the power of one-way interactive proof systems, Comput. Complexity 3 (1993), 292-305; Preliminary version appeared in "Proc. 8th Symp. on Theor. Aspects of Comp. Sci.," Lect. Notes in Comput. Sci., Springer-Verlag, New York/Berlin, pp. 456-465, 1991.
    • (1991) Lect. Notes in Comput. Sci. , pp. 456-465
  • 25
    • 0026991175 scopus 로고
    • Two-prover one-round proof systems: Their power and their problems
    • U. Feige and L. Lovász, Two-prover one-round proof systems: Their power and their problems, in "Proc. 24th ACM Symp. on Theory of Computing," pp. 733-741, 1992.
    • (1992) Proc. 24th ACM Symp. on Theory of Computing , pp. 733-741
    • Feige, U.1    Lovász, L.2
  • 30
    • 0000126406 scopus 로고
    • Minkowski's convex body theorem and integer programming
    • R. Kannan, Minkowski's convex body theorem and integer programming, Math. Oper. Res. 12 No. 3, (1987).
    • (1987) Math. Oper. Res. , vol.12 , Issue.3
    • Kannan, R.1
  • 31
    • 0000351029 scopus 로고
    • Algorithms geometry of numbers
    • (Traub, Grosz, Lampson, and Nilsson, Eds.), Publ. Annual Reviews Inc.
    • R. Kannan, Algorithms geometry of numbers, in "Annual Reviews of Computer Science" (Traub, Grosz, Lampson, and Nilsson, Eds.), Vol.2, pp. 231-267, Publ. Annual Reviews Inc., 1987.
    • (1987) Annual Reviews of Computer Science , vol.2 , pp. 231-267
    • Kannan, R.1
  • 32
    • 0003037529 scopus 로고
    • Reducibility among combinatorial problems
    • (Miller and Thatcher, Eds.), Plenum, New York
    • R. M. Karp, Reducibility among combinatorial problems, in "Complexity of Computer Computations" (Miller and Thatcher, Eds.), pp. 85-103, Plenum, New York, 1972.
    • (1972) Complexity of Computer Computations , pp. 85-103
    • Karp, R.M.1
  • 33
    • 34249953865 scopus 로고
    • Korkine Zolotarev bases and successive minima of a lattice and its reciprocal lattice
    • J. Lagarias, H. W. Lenstra, and C. P. Schnorr, Korkine Zolotarev bases and successive minima of a lattice and its reciprocal lattice, Combinatorica 10 (1990), 333-348.
    • (1990) Combinatorica , vol.10 , pp. 333-348
    • Lagarias, J.1    Lenstra, H.W.2    Schnorr, C.P.3
  • 35
    • 34250244723 scopus 로고
    • Factoring polynomials with rational coefficients
    • A. K. Lenstra, H. W. Lenstra, and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 513-534.
    • (1982) Math. Ann. , vol.261 , pp. 513-534
    • Lenstra, A.K.1    Lenstra, H.W.2    Lovász, L.3
  • 36
    • 0003528294 scopus 로고
    • An Algorithmic Theory of Numbers, Graphs and Convexity
    • SIAM, Philadelphia
    • L. Lovász, "An Algorithmic Theory of Numbers, Graphs and Convexity," NSF-CBMS Reg. Conference Series, SIAM, Philadelphia, 1986.
    • (1986) NSF-CBMS Reg. Conference Series
    • Lovász, L.1
  • 37
    • 0028514351 scopus 로고
    • On the hardness of approximating minimization problems
    • C. Lund and M. Yannakakis, On the hardness of approximating minimization problems, J. A. C. M. 41, No. 5 (1994), 960-981; prelim, version in "25th STOC," pp. 286-293, 1993.
    • (1994) J. A. C. M. , vol.41 , Issue.5 , pp. 960-981
    • Lund, C.1    Yannakakis, M.2
  • 38
    • 0028514351 scopus 로고
    • C. Lund and M. Yannakakis, On the hardness of approximating minimization problems, J. A. C. M. 41, No. 5 (1994), 960-981; prelim, version in "25th STOC," pp. 286-293, 1993.
    • (1993) 25th STOC , pp. 286-293
  • 40
    • 0026366408 scopus 로고
    • Optimization, approximation and complexity classes
    • C. Papadimitriou and M. Yannakakis, Optimization, approximation and complexity classes, J. Comput. System Sci. 43 (1991), 425-440; prelim, version in "20th ACM STOC," pp. 229-234, 1988.
    • (1991) J. Comput. System Sci. , vol.43 , pp. 425-440
    • Papadimitriou, C.1    Yannakakis, M.2
  • 41
    • 0026366408 scopus 로고
    • C. Papadimitriou and M. Yannakakis, Optimization, approximation and complexity classes, J. Comput. System Sci. 43 (1991), 425-440; prelim, version in "20th ACM STOC," pp. 229-234, 1988.
    • (1988) 20th ACM STOC , pp. 229-234
  • 42
    • 0009807286 scopus 로고
    • A hierarchy of polynomial-time basis reduction algorithms
    • (Lovász and Szemerédi, Eds.), North-Holland, Amsterdam
    • C. P. Schnorr, A hierarchy of polynomial-time basis reduction algorithms, in "Proceedings, Conf. on Algorithms, Pécs, Hungary" (Lovász and Szemerédi, Eds.), pp. 375-386 North-Holland, Amsterdam, 1985.
    • (1985) Proceedings, Conf. on Algorithms, Pécs, Hungary , pp. 375-386
    • Schnorr, C.P.1
  • 43
    • 85030049645 scopus 로고    scopus 로고
    • Approximating the number of error locations is NP-complete
    • to appear
    • J. Stern, Approximating the number of error locations is NP-complete, in "Proceedings, AAECC-10," to appear.
    • Proceedings, AAECC-10
    • Stern, J.1
  • 44
    • 0008160014 scopus 로고
    • Another NP-Complete Problem and the Complexity of Computing Short Vectors in a Lattice
    • Math. Inst., Univ. Amsterdam
    • P. van Emde Boas, "Another NP-Complete Problem and the Complexity of Computing Short Vectors in a Lattice," Tech. Report 81-04, Math. Inst., Univ. Amsterdam, 1981.
    • (1981) Tech. Report 81-04
    • Van Emde Boas, P.1


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