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Volumn 65, Issue 1, 2013, Pages 159-176

Exponential inapproximability of selecting a maximum volume sub-matrix

Author keywords

Complexity; Inapproximability; Matrices; Volume

Indexed keywords

COLUMN VECTOR; COMPLEXITY; EXPONENTIAL INAPPROXIMABILITY; INAPPROXIMABILITY; POSITIVE INTEGERS; VOLUME;

EID: 84872617323     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-011-9582-6     Document Type: Article
Times cited : (53)

References (26)
  • 1
    • 0032058198 scopus 로고    scopus 로고
    • Proof verification and the hardness of approximation problems
    • Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and the hardness of approximation problems. J. ACM 45(3), 501-555 (1998) (Pubitemid 128506634)
    • (1998) Journal of the ACM , vol.45 , Issue.3 , pp. 501-555
    • Arora, S.1    Lund, C.2    Motwani, R.3    Sudan, M.4    Szegedy, M.5
  • 2
    • 0031651077 scopus 로고    scopus 로고
    • Probabilistic checking of proofs: A new characterization of NP
    • Arora, S., Safra, S.: Probabilistic checking of proofs: a new characterization of NP. J. ACM 45(1), 70-122 (1998) (Pubitemid 128615465)
    • (1998) Journal of the ACM , vol.45 , Issue.1 , pp. 70-122
    • Arora, S.1    Safra, S.2
  • 5
    • 0002170151 scopus 로고
    • Rank revealing QR factorizations
    • 10.1016/0024-3795(87)90103-0
    • Chan, T.F.: Rank revealing QR factorizations. Linear Algebra Appl. 88/89, 67-82 (1987)
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 67-82
    • Chan, T.F.1
  • 6
    • 84985405500 scopus 로고
    • Low-rank revealing QR factorizations
    • 1269942 0804.65027 10.1002/nla.1680010105
    • Chan, T.F., Hansen, P.: Low-rank revealing QR factorizations. Numer. Linear Algebra Appl. 1, 33-44 (1994)
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 33-44
    • Chan, T.F.1    Hansen, P.2
  • 7
    • 0006770037 scopus 로고
    • On rank-revealing factorizations
    • 1266606 0796.65030 10.1137/S0895479891223781
    • Chandrasekaran, S., Ipsen, I.C.F.: On rank-revealing factorizations. SIAM J. Matrix Anal. Appl. 15, 592-622 (1994)
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 592-622
    • Chandrasekaran, S.1    Ipsen, I.C.F.2
  • 8
    • 78649910530 scopus 로고    scopus 로고
    • On selecting a maximum volume sub-matrix of a matrix and related problems
    • 1181.15002 10.1016/j.tcs.2009.06.018
    • Çivril, A., Magdon-Ismail, M.: On selecting a maximum volume sub-matrix of a matrix and related problems. Theor. Comput. Sci. 410(47-49), 4801-4811 (2009)
    • (2009) Theor. Comput. Sci. , vol.410 , Issue.47-49 , pp. 4801-4811
    • Çivril, A.1    Magdon-Ismail, M.2
  • 9
    • 33847298171 scopus 로고    scopus 로고
    • Subset selection for matrices
    • DOI 10.1016/j.laa.2006.08.034, PII S0024379506003922
    • de Hoog, F.R., Mattheijb, R.M.M.: Subset selection for matrices. Linear Algebra Appl. 422, 349-359 (2007) (Pubitemid 46329667)
    • (2007) Linear Algebra and Its Applications , vol.422 , Issue.2-3 , pp. 349-359
    • De Hoog, F.R.1    Mattheij, R.M.M.2
  • 11
    • 45849092005 scopus 로고    scopus 로고
    • Matrix approximation and projective clustering via volume sampling
    • 2322879 10.4086/toc.2006.v002a012
    • Deshpande, A., Rademacher, L., Vempala, S., Wang, G.: Matrix approximation and projective clustering via volume sampling. Theory Comput. 2(1), 225-247 (2006)
    • (2006) Theory Comput. , vol.2 , Issue.1 , pp. 225-247
    • Deshpande, A.1    Rademacher, L.2    Vempala, S.3    Wang, G.4
  • 13
    • 0032108328 scopus 로고    scopus 로고
    • A Threshold of ln n for Approximating Set Cover
    • Feige, U.: A threshold of lnn for approximating set cover. J. ACM 45(4), 634-652 (1998) (Pubitemid 128488790)
    • (1998) Journal of the ACM , vol.45 , Issue.4 , pp. 634-652
    • Feige, U.1
  • 15
    • 0004236492 scopus 로고    scopus 로고
    • Johns Hopkins University Press Baltimore 0865.65009
    • Golub, G.H., Loan, C.V.: Matrix Computations. Johns Hopkins University Press, Baltimore (1996)
    • (1996) Matrix Computations
    • Golub, G.H.1    Loan, C.V.2
  • 16
    • 0037790752 scopus 로고    scopus 로고
    • The maximal-volume concept in approximation by low-rank matrices
    • 280 AMS Providence
    • Goreinov, S.A., Tyrtyshnikov, E.E.: The maximal-volume concept in approximation by low-rank matrices. In: Contemporary Mathematics, vol. 280, pp. 47-51. AMS, Providence (2001)
    • (2001) Contemporary Mathematics , pp. 47-51
    • Goreinov, S.A.1    Tyrtyshnikov, E.E.2
  • 17
    • 48249131944 scopus 로고    scopus 로고
    • Pseudo-skeleton approximations by matrices of maximal volume
    • 1620099 10.4213/mzm1644
    • Goreinov, S.A., Zamarashkin, N.L., Tyrtyshnikov, E.E.: Pseudo-skeleton approximations by matrices of maximal volume. Mat. Zametki 62, 619-623 (1997)
    • (1997) Mat. Zametki , vol.62 , pp. 619-623
    • Goreinov, S.A.1    Zamarashkin, N.L.2    Tyrtyshnikov, E.E.3
  • 18
    • 51249169029 scopus 로고
    • Largest j-simplices n-polytopes
    • 1318791 0826.52014 10.1007/BF02574058
    • Gritzmann, P., Klee, V., Larman, D.G.: Largest j-simplices n-polytopes. Discrete Comput. Geom. 13, 477-515 (1995)
    • (1995) Discrete Comput. Geom. , vol.13 , pp. 477-515
    • Gritzmann, P.1    Klee, V.2    Larman, D.G.3
  • 19
    • 0003216822 scopus 로고    scopus 로고
    • Efficient algorithms for computing a strong rank-revealing QR factorization
    • Gu, M., Eisenstat, S.C.: Efficient algorithms for computing a strong rank-revealing QR factorization. SIAM J. Sci. Comput. 17(4), 848-869 (1996) (Pubitemid 126621180)
    • (1996) SIAM Journal of Scientific Computing , vol.17 , Issue.4 , pp. 848-869
    • Gu, M.1    Eisenstat, S.C.2
  • 20
    • 33646508996 scopus 로고    scopus 로고
    • On the complexity of approximating k-Set Packing
    • DOI 10.1007/s00037-006-0205-6
    • Hazan, E., Safra, S., Schwartz, O.: On the complexity of approximating k-set packing. Comput. Complex. 15, 20-39 (2006) (Pubitemid 43706824)
    • (2006) Computational Complexity , vol.15 , Issue.1 , pp. 20-39
    • Hazan, E.1    Safra, S.2    Schwartz, O.3
  • 21
    • 84968501766 scopus 로고
    • Rank-revealing QR factorizations and the singular value decomposition
    • 1106970 0743.65037
    • Hong, Y.P., Pan, C.T.: Rank-revealing QR factorizations and the singular value decomposition. Math. Comput. 58, 213-232 (1992)
    • (1992) Math. Comput. , vol.58 , pp. 213-232
    • Hong, Y.P.1    Pan, C.T.2
  • 22
    • 33745662129 scopus 로고    scopus 로고
    • Parameterized complexity and improved inapproximability for computing the largest j-simplex in a V-polytope
    • DOI 10.1016/j.ipl.2006.05.006, PII S0020019006001487
    • Koutis, I.: Parameterized complexity and improved inapproximability for computing the largest j-simplex in a V-polytope. Inf. Process. Lett. 100, 8-13 (2006) (Pubitemid 43975099)
    • (2006) Information Processing Letters , vol.100 , Issue.1 , pp. 8-13
    • Koutis, I.1
  • 23
    • 0242570402 scopus 로고    scopus 로고
    • Polynomial-time approximation of largest simplices in V-polytopes
    • 2019499 1165.68524 10.1016/S0166-218X(03)00226-9
    • Packer, A.: Polynomial-time approximation of largest simplices in V-polytopes. Discrete Appl. Math. 134, 213-237 (2004)
    • (2004) Discrete Appl. Math. , vol.134 , pp. 213-237
    • Packer, A.1
  • 24
    • 0034392123 scopus 로고    scopus 로고
    • On the existence and computation of rank-revealing LU factorizations
    • 1782425 0962.65023 10.1016/S0024-3795(00)00120-8
    • Pan, C.T.: On the existence and computation of rank-revealing LU factorizations. Linear Algebra Appl. 316(1-3), 199-222 (2000)
    • (2000) Linear Algebra Appl. , vol.316 , Issue.1-3 , pp. 199-222
    • Pan, C.T.1
  • 25
    • 0001972217 scopus 로고    scopus 로고
    • Bounds on singular values revealed by QR factorizations
    • 1735102 0944.65042 10.1023/A:1022395308695
    • Pan, C.T., Tang, P.T.P.: Bounds on singular values revealed by QR factorizations. BIT Numer. Math. 39, 740-756 (1999)
    • (1999) BIT Numer. Math. , vol.39 , pp. 740-756
    • Pan, C.T.1    Tang, P.T.P.2
  • 26
    • 0001226672 scopus 로고    scopus 로고
    • A parallel repetition theorem
    • Raz, R.: A parallel repetition theorem. SIAM J. Comput. 27(3), 763-803 (1998) (Pubitemid 128490838)
    • (1998) SIAM Journal on Computing , vol.27 , Issue.3 , pp. 763-803
    • Raz, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.