Erratum to: Graph matching using the interference of continuous-time quantum walks [Pattern Recognition 42 (5) 985-1002] (DOI:10.1016/j.patcog.2008.09.001);Graph matching using the interference of continuous-time quantum walks

Pattern Recognition

Volumn 42, Issue 5, 2009, Pages 985-1002

  Emms, David ^a   Wilson, Richard C ^a   Hancock, Edwin R ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

Author keywords

Continuous time quantum walk; Graph matching; Interference; Object recognition

Indexed keywords

CONTINUOUS TIME SYSTEMS; GRAPHIC METHODS; ITERATIVE METHODS; OBJECT RECOGNITION; PATTERN MATCHING; PROBABILITY; WAVE INTERFERENCE;

CONSISTENCY MEASURES; CONTINUOUS-TIME QUANTUM WALKS; GRAPH MATCHINGS; GRAPH SIMILARITY; INEXACT GRAPH MATCHING; ITERATIVE TECHNIQUE; QUANTUM INTERFERENCE; REAL-WORLD GRAPHS;

GRAPH THEORY;

EID: 58249085186     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2009.01.029     Document Type: Erratum

References (45)

1. J. Köbler, On graph isomorphism for restricted graph classes, in: CiE, 2006, pp. 241-256.
2. L. Babai, D.Yu. Grigoryev, D.M. Mount, Isomorphism of graphs with bounded eigenvalue multiplicity, in: STOC '82: Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, ACM Press, New York, NY, USA, 1982, pp. 310-324.
3. J.E. Hopcroft, J.K. Wong, A linear time algorithm for isomorphism of planar graphs, in: Proceedings of the 6th Annual ACM Symposium on the Theory of Computing (STOC'74), 1974, pp. 172-184.
4. McKay B.D. Practical graph isomorphism. Congr. Numer. 30 (1981) 45-87
5. T. Miyazaki, The complexity of McKay's canonical labeling algorithm, Groups and Computation. II, in: L. Finkelstein, W.M. Kantor (Eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 28, American Mathematical Society, Providence, Rhode Island, 1997, pp. 239-256. MR1444139 (98c:05119).
6. Ullmann J.R. An algorithm for subgraph isomorphism. J. ACM 23 1 (1976) 31-42
7. Luo B., and Hancock E.R. Structural graph matching using the EM algorithm and singular value decomposition. Pattern Anal. Mach. Intell. 23 10 (2001) 1120-1136
8. A. Robles-Kelly, E. Hancock, Graph matching using spectral seriation and string edit distance, in: GbRPR 2003, 2003.
9. Messmer B.T., and Bunke H. A decision tree approach to graph and subgraph isomorphism detection. Pattern Recognition 32 12 (1999) 1979-1998
10. Sanfeliu A., and Fu K.-S. A distance measure between attributed relational graphs for pattern recognition. IEEE Trans. Systems, Man Cybern. 13 (1983) 353-362
11. Christmas W.J., Kittler J., and Petrou M. Structural matching in computer vision using probabilistic relaxation. IEEE Trans. Pattern Anal. Mach. Intell. 17 8 (1995) 749-764
12. Shapiro L.G., and Haralick R.M. Organization of relational models for scene analysis. IEEE Trans. Pattern Anal. Mach. Intell. 4 6 (1982) 595-602
13. Eshera M.A., and Fu K.S. A graph distance measure for image analysis. IEEE Trans. Systems, Man Cybern. 14 3 (1984) 398-408
14. Horaud R., and Skordas T. Stereo correspondence through feature grouping and maximal cliques. IEEE Trans. Pattern Anal. Mach. Intell. 11 11 (1989) 1168-1180
15. Bunke H. On a relation between graph edit distance and maximum common subgraph. Pattern Recognition Lett. 18 9 (1997) 689-694
16. Robles-Kelly A., and Hancock E.R. Graph edit distance from spectral seriation. IEEE Trans. Pattern Anal. Mach. Intell. 27 3 (2005) 365-378
17. L. Grover, A fast quantum mechanical algorithm for database search, in: Proceedings of the 28th Annual ACM Symposium on the Theory of Computation, New York, NY, ACM Press, New York, 1996, pp. 212-219.
18. Shor P.W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26 (1997) 1484-1509
19. Nielson M.A., and Chuang I.L. Quantum Computing and Quantum Information (2000), Cambridge University Press, Cambridge
20. Jozsa R. Quantum factoring, discrete logarithms, and the hidden subgroup problem. Comput. Sci. Eng. 3 2 (2001) 34-43
21. Duncan A.J., Batty M., Braunstein S.L., and Rees S. Quantum algorithms in group theory. Contemp. Math. 349 (2004) 1-62
22. R. Beals. Quantum computation of Fourier transforms over symmetric groups, in: Proceedings of the 29th Annual ACM Symposium on the Theory of Computation (STOC), Texas, ACM Press, New York, 1997, pp. 48-53.
23. J. Kempe, A. Shalev, The hidden subgroup problem and permutation group theory, in: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Vancouver, British Columbia, 2005, pp. 1118-1125, ISBN:0-89871-585-7.
24. M. Ettinger, P. Høyer, A quantum observable for the graph isomorphism problem, 1999, arXiv:quant-ph/9901029.
25. Kempe J. Quantum random walks-an introductory overview. Contemp. Phys. 44 4 (2003) 307-327
26. Farhi E., and Gutmann S. Quantum computation and decision trees. Phys. Rev. A 58 (1998) 915-928
27. D. Aharonov, A. Ambainis, J. Kempe, U. Vazirani, Quantum walks on graphs, in: STOC '01: Proceedings of the ACM Theory of Computing, ACM Press, New York, 2001, pp. 50-59.
28. A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, J. Watrous, One-dimensional quantum walks, in: Proceedings of the 33th STOC, New York, NY, ACM, New York, 2001, pp. 60-69.
29. J. Kempe, Quantum random walks hit exponentially faster, in: Proceedings of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM'03), 2003, pp. 354-369.
30. Childs A., Farhi E., and Gutmann S. An example of the difference between quantum and classical random walks. Quantum Inf. Process. 1 (2002) 35
31. A.M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, D.A. Spielman, Exponential algorithmic speedup by a quantum walk, in: STOC '03: Proceedings of the 35th ACM Symposium on TOC, New York, NY, USA, ACM Press, New York, 2003, pp. 59-68.
32. V. Gudkov, S. Nussinov, Graph equivalence and characterization via a continuous evolution of a physical analog, 2002 (cond-mat/0209112).
33. Shiau S.Y., Joynt R., and Coppersmith S.N. Physically-motivated dynamical algorithms for the graph isomorphism problem. Quantum Inf. Comput. 5 6 (2005) 492-506
34. T. Rudolph, Constructing physically intuitive graph invariants, 2002 (quant-ph/0206068).
35. Sarti L., Maggini M., and Gori M. Exact and approximate graph matching using random walks. IEEE Trans. Pattern Anal. Mach. Intell. 27 7 (2005) 1100-1111
36. Kuhn H.W. The Hungarian method for the assignment problem. Naval Res. Logistic Q. 2 (1955) 83-97
37. Barrow H.G., and Burstall R.M. Subgraph isomorphism, matching relational structures and maximal cliques. Inf. Process. Lett. 4 4 (1976) 83-84
38. Barrow H.G., and Burstall R.M. Subgraph isomorphism, matching relational structures and maximal cliques. Inf. Process. Lett. 4 (1976) 83-84
39. Pelillo M. Relaxation labelling networks for the maximum clique problem. J. Artif. Neural Networks 2 4 (1995) 313-328
40. Umeyama S. An eigen decomposition approach to weighted graph matching problems. Pattern Anal. Mach. Intell. 10 5 (1988) 695-703
41. Zhang F., and Hancock E.R. Graph spectral image smoothing using the heat kernel. Pattern Recognition 41 11 (2008) 3328-3342
42. Gold S., and Rangarajan A. A graduated assignment algorithm for graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 18 4 (1996) 377-388
43. Wilson R.C., and Hancock E.R. Structural matching by discrete relaxation. IEEE Trans. Pattern Anal. Mach. Intell. 19 6 (1997) 634-648
44. Scott G., and Longuet-Higgins H. An algorithm for associating the features of two patterns. Proc. R. Soc. London B 244 (1991)
45. Douglas B.L., and Wang J.B. A classical approach to the graph isomorphism problem. J. Phys. A Math. Theor. 41 (2008) 1-15