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Volumn 5, Issue 6, 2005, Pages 492-506

Physically-motivated dynamical algorithms for the graph isomorphism problem

Author keywords

Graph isomorphism; Quantum computing

Indexed keywords

COMPUTATIONAL CHEMISTRY; DYNAMICAL SYSTEMS; GRAPH STRUCTURES; GRAPH THEORY; POLYNOMIAL APPROXIMATION; QUANTUM COMPUTERS; SET THEORY;

EID: 23744480284     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (38)

References (34)
  • 2
    • 0008690083 scopus 로고    scopus 로고
    • The graph isomorphism problem
    • Dept. of Computing Science, University of Alberta
    • S. Fortin, The graph isomorphism problem, Tech. Report TR 96-20, Dept. of Computing Science, University of Alberta, 1996.
    • (1996) Tech. Report , vol.TR 96-20
    • Fortin, S.1
  • 3
    • 84986520524 scopus 로고
    • The graph isomorphism problem
    • X. Liu and D.J. Klein, The graph isomorphism problem, J. Comput. Chem. 12, 1243-1251 (1991).
    • (1991) J. Comput. Chem. , vol.12 , pp. 1243-1251
    • Liu, X.1    Klein, D.J.2
  • 6
    • 0020166327 scopus 로고
    • Isomorphism of graphs of bounded valence can be tested in polynomial time
    • Luks, E.M., Isomorphism of graphs of bounded valence can be tested in polynomial time, J. Comput. Sys. Sci. 25, 42-65 (1982)
    • (1982) J. Comput. Sys. Sci. , vol.25 , pp. 42-65
    • Luks, E.M.1
  • 9
    • 0344349316 scopus 로고
    • A linear-time algorithm for isomorphism of graphs of bounded average genus
    • J. Chen, A linear-time algorithm for isomorphism of graphs of bounded average genus, SIAM J. Disc. Math. 7, 614-631 (1994).
    • (1994) SIAM J. Disc. Math. , vol.7 , pp. 614-631
    • Chen, J.1
  • 11
    • 0001460788 scopus 로고
    • A note on the graph isomorphism counting problem
    • R. Mathon, A note on the graph isomorphism counting problem, Information Processing Letters, 8, 131-132 (1979).
    • (1979) Information Processing Letters , vol.8 , pp. 131-132
    • Mathon, R.1
  • 13
    • 0024128620 scopus 로고
    • Graph isomorphism is in the low hierarchy
    • U. Schöning, Graph isomorphism is in the low hierarchy, J. Computer and System Sciences 37, 312-323 (1988).
    • (1988) J. Computer and System Sciences , vol.37 , pp. 312-323
    • Schöning, U.1
  • 14
    • 23744436646 scopus 로고    scopus 로고
    • note
    • Perhaps the best-known example of a problem believed to be neither in P nor NP-complete is factorization, for which no classical polynomial algorithm is known but which can be solved in polynomial time on a quantum computer [15].
  • 15
    • 0142051871 scopus 로고    scopus 로고
    • Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
    • P.W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Sci. Statis. Comput. 26, 1484 (1997).
    • (1997) SIAM J. Sci. Statis. Comput. , vol.26 , pp. 1484
    • Shor, P.W.1
  • 17
    • 0141534114 scopus 로고    scopus 로고
    • The hidden subgroup problem and quantum computation using group representations
    • S. Hallgren, A. Russell, and A. Ta-Shma, The hidden subgroup problem and quantum computation using group representations, SIAM J. Comput. 32, 916-934 (2003).
    • (2003) SIAM J. Comput. , vol.32 , pp. 916-934
    • Hallgren, S.1    Russell, A.2    Ta-Shma, A.3
  • 20
    • 0036036708 scopus 로고    scopus 로고
    • Quantum lower bound for the collision problem
    • Aaronson Quantum Lower Bound for the Collision Problem in Proc. ACM Symp. on Theory of Computing, 635-642 (2002).
    • (2002) Proc. ACM Symp. on Theory of Computing , pp. 635-642
    • Aaronson1
  • 21
    • 23744475526 scopus 로고    scopus 로고
    • note
    • A well-known quantum algorithm motivated by physical processes is the adiabatic algorithm proposed by Farhi and collaborators [22, 23, 24]. The algorithms we examine are clearly different than the adiabatic algorithm, but the philosophy underlying the scheme is analogous.
  • 22
    • 0035917832 scopus 로고    scopus 로고
    • A quantum adiabatic algorithm applied to random instances of an NP-complete problem
    • E. Farhi et al., A quantum adiabatic algorithm applied to random instances of an NP-complete problem, Science 292, 472-475 (2001).
    • (2001) Science , vol.292 , pp. 472-475
    • Farhi, E.1
  • 23
    • 0036146412 scopus 로고    scopus 로고
    • Robustness of adiabatic quantum computation
    • A.M. Childs, E. Farhi, and J. Preskill, Robustness of adiabatic quantum computation, Phys. Rev. A 65, 012322 (2002).
    • (2002) Phys. Rev. A , vol.65 , pp. 012322
    • Childs, A.M.1    Farhi, E.2    Preskill, J.3
  • 24
    • 0036542418 scopus 로고    scopus 로고
    • Quantum search by local adiabatic evolution
    • J. Roland and N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65, 042308 (2002).
    • (2002) Phys. Rev. A , vol.65 , pp. 042308
    • Roland, J.1    Cerf, N.J.2
  • 33
    • 0037770172 scopus 로고    scopus 로고
    • Adiabatic quantum state generation and statistical zero knowledge
    • Aharonov and Ta-Shma, Adiabatic Quantum State Generation and Statistical Zero Knowledge, in Proc. ACM Symp. on Theory of Computing, 20-29 (2003).
    • (2003) Proc. ACM Symp. on Theory of Computing , pp. 20-29
    • Aharonov1    Ta-Shma2
  • 34
    • 85111345508 scopus 로고    scopus 로고
    • note
    • p > 2.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.