메뉴 건너뛰기




Volumn 46, Issue 1, 2010, Pages 9-26

On the complexity of matrix rank and rigidity

Author keywords

Complexity classes; Determinant; Matrix rank; Matrix rigidity

Indexed keywords

COMPUTATIONAL COMPLEXITY; RIGIDITY;

EID: 72249083804     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-008-9136-8     Document Type: Article
Times cited : (7)

References (36)
  • 1
    • 84887465752 scopus 로고    scopus 로고
    • Bounded-depth arithmetic circuits: Counting and closure
    • Lecture Notes in Computer Science, Berlin: Springer
    • Allender, E., Ambainis, A., Mix Barrington, D. A., Datta, S., LeThanh, H.: Bounded-depth arithmetic circuits: counting and closure. In: Proc. 26th ICALP. Lecture Notes in Computer Science, vol. 1644, pp. 149-158. Springer, Berlin (1999).
    • (1999) Proc. 26th ICALP , vol.1644 , pp. 149-158
    • Allender, E.1    Ambainis, A.2    Mix Barrington, D.A.3    Datta, S.4    Lethanh, H.5
  • 2
    • 0041993930 scopus 로고    scopus 로고
    • Arithmetic complexity, Kleene closure, and formal power series
    • Allender, E., Arvind, V., Mahajan, M.: Arithmetic complexity, Kleene closure, and formal power series. Theory Comput. Syst. 36(4), 303-328 (2003).
    • (2003) Theory Comput. Syst. , vol.36 , Issue.4 , pp. 303-328
    • Allender, E.1    Arvind, V.2    Mahajan, M.3
  • 3
    • 0033478153 scopus 로고    scopus 로고
    • The complexity of matrix rank and feasible systems of linear equations
    • Allender, E., Beals, R., Ogihara, M.: The complexity of matrix rank and feasible systems of linear equations. Comput. Complex. 8(2), 99-126 (1999).
    • (1999) Comput. Complex. , vol.8 , Issue.2 , pp. 99-126
    • Allender, E.1    Beals, R.2    Ogihara, M.3
  • 4
    • 0034563805 scopus 로고    scopus 로고
    • A compendium of problems complete for symmetric logarithmic space
    • Àlvarez, C., Greenlaw, R.: A compendium of problems complete for symmetric logarithmic space. Comput. Complex., 9, 73-95 (2000).
    • (2000) Comput. Complex. , vol.9 , pp. 73-95
    • Àlvarez, C.1    Greenlaw, R.2
  • 5
    • 33750063099 scopus 로고    scopus 로고
    • Arithmetic circuits and counting complexity classes
    • Quaderni di Matematica, J. Krajicek (Ed.), Napoli: Seconda Universita di Napoli
    • Allender, E.: Arithmetic circuits and counting complexity classes. In: Krajicek, J. (ed.) Complexity of Computations and Proofs. Quaderni di Matematica, vol. 13, pp. 33-72. Seconda Universita di Napoli, Napoli (2004).
    • (2004) Complexity of Computations and Proofs , vol.13 , pp. 33-72
    • Allender, E.1
  • 6
    • 0030554482 scopus 로고    scopus 로고
    • Relationships among PL, #l, and the determinant
    • Allender, E., Ogihara, M.: Relationships among PL, #l, and the determinant. RAIRO Theor. Inform. Appl. 30(1), 1-21 (1996).
    • (1996) RAIRO Theor. Inform. Appl. , vol.30 , Issue.1 , pp. 1-21
    • Allender, E.1    Ogihara, M.2
  • 8
    • 0032679680 scopus 로고    scopus 로고
    • The computational complexity of some problems of linear algebra
    • Buss, J. F., Frandsen, G. S., Shallit, J.: The computational complexity of some problems of linear algebra. J. Comput. Syst. Sci. 58, 572-596 (1999).
    • (1999) J. Comput. Syst. Sci. , vol.58 , pp. 572-596
    • Buss, J.F.1    Frandsen, G.S.2    Shallit, J.3
  • 10
    • 0009632171 scopus 로고
    • Problems complete for L
    • Cook, S. A., McKenzie, P.: Problems complete for L. J. Algorithms 8, 385-394 (1987).
    • (1987) J. Algorithms , vol.8 , pp. 385-394
    • Cook, S.A.1    McKenzie, P.2
  • 12
    • 0034378311 scopus 로고    scopus 로고
    • A note on nonnegative diagonally dominant matrices
    • Dahl, G.: A note on nonnegative diagonally dominant matrices. Linear Algebra Appl. 317, 217-224 (1999).
    • (1999) Linear Algebra Appl. , vol.317 , pp. 217-224
    • Dahl, G.1
  • 13
    • 0038585401 scopus 로고
    • (#L)
    • Fachbereich Informatik der Humboldt-Universität zu Berlin
    • Damm, C.: DET = L(#L). Technical Report Informatik-Preprint 8, Fachbereich Informatik der Humboldt-Universität zu Berlin (1991).
    • (1991) Technical Report Informatik-Preprint 8
    • Damm, C.1
  • 15
    • 0039627817 scopus 로고    scopus 로고
    • Maximum rank matrix completion
    • Geelen, J. F.: Maximum rank matrix completion. Linear Algebra Appl. 288(1-3), 211-217 (1999).
    • (1999) Linear Algebra Appl. , vol.288 , Issue.1-3 , pp. 211-217
    • Geelen, J.F.1
  • 19
    • 3042743084 scopus 로고    scopus 로고
    • Matrix completion problems
    • C. A. Floudas and P. M. Pardalos (Eds.), Dordrecht: Kluwer
    • Laurent, M.: Matrix completion problems. In: Floudas, C. A., Pardalos, P. M. (eds.) The Encyclopedia of Optimization, vol. 3, pp. 221-229. Kluwer, Dordrecht (2001).
    • (2001) The Encyclopedia of Optimization , vol.3 , pp. 221-229
    • Laurent, M.1
  • 20
    • 0029488086 scopus 로고
    • Spectral methods for matrix rigidity with applications to size-depth tradeoffs and communication complexity
    • Lokam, S. V.: Spectral methods for matrix rigidity with applications to size-depth tradeoffs and communication complexity. In: Proc. 36th FOCS, pp. 6-15, 1995; J. Comput. Syst. Sci. 63(3): 449-473 (2001).
    • (1995) Proc. 36th FOCS , pp. 6-15
    • Lokam, S.V.1
  • 21
    • 0035521408 scopus 로고    scopus 로고
    • J. Comput. Syst. Sci. 63(3): 449-473 (2001).
    • (2001) J. Comput. Syst. Sci. , vol.63 , Issue.3 , pp. 449-473
  • 22
    • 0004015440 scopus 로고
    • The Prindle, Weber and Schmidt Complementary Series in Mathematics, Boston: Allyn and Bacon
    • Marcus, M., Minc, H.: A Survey of Matrix Theory and Matrix inequalities. The Prindle, Weber and Schmidt Complementary Series in Mathematics, vol. 14. Allyn and Bacon, Boston (1964).
    • (1964) A Survey of Matrix Theory and Matrix Inequalities , vol.14
    • Marcus, M.1    Minc, H.2
  • 23
    • 51249173165 scopus 로고
    • A fast parallel algorithm to compute the rank of a matrix over an arbitrary field
    • Mulmuley, K.: A fast parallel algorithm to compute the rank of a matrix over an arbitrary field. Combinatorica 7, 101-104 (1987).
    • (1987) Combinatorica , vol.7 , pp. 101-104
    • Mulmuley, K.1
  • 24
    • 0009117949 scopus 로고
    • Mixed matrices-irreducibility and decomposition
    • The IMA Volumes in Mathematics and Its Applications, R. A. Brualdi, S. Friedland, and V. Klee (Eds.), Berlin: Springer
    • Murota, K.: Mixed matrices-irreducibility and decomposition. In: Brualdi, R. A., Friedland, S., Klee, V. (eds.) Combinatorial and Graph-Theoretic Problems in Linear Algebra. The IMA Volumes in Mathematics and Its Applications, vol. 50, pp. 39-71. Springer, Berlin (1993).
    • (1993) Combinatorial and Graph-Theoretic Problems in Linear Algebra , vol.50 , pp. 39-71
    • Murota, K.1
  • 25
  • 27
    • 0027307460 scopus 로고
    • Checking robust nonsingularity is NP-hard
    • Poljak, S., Rohn, J.: Checking robust nonsingularity is NP-hard. Math. Control Signals Syst. 6, 1-9 (1993).
    • (1993) Math. Control Signals Syst. , vol.6 , pp. 1-9
    • Poljak, S.1    Rohn, J.2
  • 28
    • 34848865701 scopus 로고    scopus 로고
    • Undirected st-conenctivity in logspace
    • Reingold, O.: Undirected st-conenctivity in logspace. In Proc. 37th STOC, pp. 376-385 (2005).
    • (2005) Proc. 37th STOC , pp. 376-385
    • Reingold, O.1
  • 29
    • 0003113960 scopus 로고
    • Systems of linear interval equations
    • Rohn, J.: Systems of linear interval equations. Linear Algebra Appl. 126, 39-78 (1989).
    • (1989) Linear Algebra Appl. , vol.126 , pp. 39-78
    • Rohn, J.1
  • 30
    • 0009221638 scopus 로고
    • Checking positive definiteness or stability of symmetric interval matrices is NP-hard
    • Rohn, J.: Checking positive definiteness or stability of symmetric interval matrices is NP-hard. Comment. Math. Univ. Carol. 35, 795-797 (1994).
    • (1994) Comment. Math. Univ. Carol. , vol.35 , pp. 795-797
    • Rohn, J.1
  • 32
  • 33
    • 85016972944 scopus 로고
    • Graph theoretic arguments in low-level complexity
    • Lecture Notes in Computer Science, Berlin: Springer
    • Valiant, L. G.: Graph theoretic arguments in low-level complexity. In: Proc. 6th MFCS. Lecture Notes in Computer Science, vol. 53, pp. 162-176. Springer, Berlin (1977).
    • (1977) Proc. 6th MFCS , vol.53 , pp. 162-176
    • Valiant, L.G.1
  • 35
    • 0026375502 scopus 로고
    • Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits
    • Lecture Notes in Computer Science, Berlin: Springer
    • Vinay, V.: Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits. In: Proc. 6th Structure in Complexity Theory Conference. Lecture Notes in Computer Science, vol. 223, pp. 270-284. Springer, Berlin (1991).
    • (1991) Proc. 6th Structure in Complexity Theory Conference , vol.223 , pp. 270-284
    • Vinay, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.