Isomorphism identification of graphs: Especially for the graphs of kinematic chains

Mechanism and Machine Theory

Volumn 44, Issue 1, 2009, Pages 122-139

  Ding, Huafeng ^a   Huang, Zhen ^a  

^a YANSHAN UNIVERSITY   (China)

Author keywords

Characteristic adjacency matrix; Isomorphism identification; Kinematic chains; The perimeter graph

Indexed keywords

BOOLEAN FUNCTIONS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; COMPUTER SCIENCE; KINEMATICS; MATHEMATICAL TECHNIQUES; MATRIX ALGEBRA; SET THEORY; TREES (MATHEMATICS);

ADJACENCY MATRIXES; CHALLENGING PROBLEMS; CHARACTERISTIC ADJACENCY MATRIX; COMPUTATIONAL COMPLEXITY ANALYSIS; EFFICIENT; ISOMORPHISM IDENTIFICATION; ISOMORPHISM IDENTIFICATIONS; KINEMATIC CHAINS; MATHEMATICS; NEW ALGORITHMS; OF GRAPHS; RELABELLING; SKETCHING; THE PERIMETER GRAPH;

GRAPH THEORY;

EID: 54249152900     PISSN: 0094114X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmachtheory.2008.02.008     Document Type: Article

References (40)

1. Luks E.M. Isomorphism of graphs of bounded valence can be tested in polynomial time. J. Comput. Syst. Sci. 25 1 (1982) 42-65
2. Abdulrahim M., and Misra M. A graph isomorphism algorithm for object recognition. Pattern Anal. Appl. 1 3 (1998) 189-201
3. Messmer B.T., and Bunke H. A decision tree approach to graph and subgraph isomorphism detection. Pattern Recogn. 32 12 (1999) 1979-1998
4. Schmidt D.C., and Druffel L.E. Fast backtracking algorithm to test directed graphs for isomorphism using distance matrices. J. Assoc. Comput. Mach. 23 3 (1976) 433-445
5. Ullmann J.R. An algorithm for subgraph isomorphism. J. Assoc. Comput. Mach. 23 1 (1976) 31-42
6. Cordella L.P., Foggia P., Sansone C., and Vento M. Subgraph transformations for the inexact matching of attributed relational graphs. Comput. Suppl. 12 1 (1998) 43-52
7. L.P. Cordella, P. Foggia, C. Sansone, M. Vento, An improved algorithm for matching large graphs, in: Proceedings of the Third IAPR-TC-15 International Workshop on Graph-based Representations, Italy, 2001, pp. 149-159.
8. McKay B.D. Practical graph isomorphism. Congressus Numerantium 30 1 (1981) 45-87
9. Eric A.B., and Chris H. Efficient enumeration and hierarchical classification of planar simple-jointed kinematic chains: application to 12- and 14-bar single degree-of-freedom chains. Mech. Mach. Theory 40 9 (2005) 1030-1050
10. Rajesh P.S., and Linda C.S. Structural synthesis of planar kinematic chains by adapting a Mckay-type algorithm. Mech. Mach. Theory 41 9 (2006) 1021-1030
11. Uicker J.J., and Raicu A. A method for the identification of and recognition of equivalence of kinematic chains. Mech. Mach. Theory 10 5 (1975) 375-383
12. Yan H.S., and Hall A.S. Linkage characteristic polynomials: definitions, coefficients by inspection. ASME J. Mech. Des. 103 3 (1981) 578-584
13. Yan H.S., and Hall A.S. Linkage characteristic polynomials: assembly, theorems, uniqueness. ASME J. Mech. Des. 104 1 (1982) 11-20
14. Mruthyunjaya T.S. A computerized methodology for structural synthesis of kinematic chains: Part 1 - Formulation. Mech. Mach. Theory 19 6 (1984) 487-495
15. Mruthyunjaya T.S. A computerized methodology for structural synthesis of kinematic chains: Part 2 - Application to several fully or partial known cases. Mech. Mach. Theory 19 6 (1984) 497-505
16. Mruthyunjaya T.S. A computerized methodology for structural synthesis of kinematic chains: Part 3 - Application to new case of 10-link, three-freedom chains. Mech. Mach. Theory 19 6 (1984) 507-530
17. Mruthyunjaya T.S., and Balasubramanzan H.R. In quest of a reliable and efficient computational test for detection of isomorphism in kinematic chains. Mech. Mach. Theory 22 2 (1987) 131-140
18. Sohn W.J., and Freudenstein F. Application of dual graphs to the automatic generation of the kinematic structures of mechanisms. ASME J. Mech. Des. 108 (1986) 392-398
19. A. Ambekar, V. Agrawal, On canonical numbering of kinematic chains and isomorphism problem: max code, in: ASME Mechanisms Conference, 1986.
20. Ambekar A.G., and Agrawal V.P. Canonical numbering of kinematic chains and isomorphism problem: min code. Mech. Mach. Theory 22 5 (1987) 453-461
21. Tang C., and Liu T. Degree code; a new mechanism identifier. ASME J. Mech. Des. 115 3 (1993) 627-630
22. Shin J.K., and Krishnamurty S. On identification and canonical numbering of pin jointed kinematic chains. ASME J. Mech. Des. 116 1 (1994) 182-188
23. Shin J.K., and Krishnamurty S. Development of a standard code for colored graphs and its application to kinematic chains. ASME J. Mech. Des. 114 1 (1992) 189-196
24. Rao A.C., and Varada R.D. Application of the hamming number technique to detect isomorphism among kinematic chains and inversion. Mech. Mach. Theory 26 1 (1991) 55-75
25. Rao A.C., and Rao C.N. Loop based pseudo hamming values - 1. Testing isomorphism and rating kinematic chains. Mech. Mach. Theory 28 1 (1992) 113-127
26. Rao A.C., and Rao C.N. Loop based pseudo hamming values - 2. Inversions, preferred frames and actuator. Mech. Mach. Theory 28 1 (1992) 129-143
27. Chu J.K., and Cao W.Q. Identification of isomorphism among kinematic chains and inversions using link's adjacent chain table. Mech. Mach. Theory 29 1 (1994) 53-58
28. Rao A.C. Application of fuzzy logic for the study of isomorphism, inversions, symmetry, parallelism and mobility in kinematic chains. Mech. Mach. Theory 35 8 (2000) 1103-1116
29. P.R. He, W.J. Zhang, Q. Li, A quadraticform-based approach to identification of kinematic chains in structural analysis and synthesis of mechanisms, in: Proceedings of the 2001 ASME Design Engineering Technical Conferences and Computers and Information Engineering Conference, DETC2001/DAC-21067, Pittsburgh, PA, USA, September 2001, 2001.
30. P.R. He, W.J. Zhang, Q. Li, Eigenvalues and eigenvectors information of graph and their validity in identification of graph isomorphism, in: ASME 2002 Design Engineering Technical Conferences and Computers and Information Engineering Conference, DETC2002/MECH-342147, Montreal, Canada, September 29-October 2, 2002.
31. He P.R., Zhang W.J., Li Q., et al. A new method for detection of graph isomorphism based on the quadratic form. ASME J. Mech. Des. 125 3 (2003) 640-642
32. He P.R., Zhang W.J., and Li Q. Some further development on the eigensystem approach for graph isomorphism detection. Journal of the Franklin Institute 342 6 (2005) 657-673
33. Chang Z.Y., Zhang C., Yang Y.H., et al. A new method to mechanism kinematic chain isomorphism identification. Mech. Mach. Theory 37 4 (2002) 411-417
34. Cubillo J.P., and Wan J.B. Comments on mechanism kinematic chain isomorphism identification using adjacent matrices. Mech. Mach. Theory 40 2 (2005) 131-139
35. Rajesh P.S., and Linda C.S. Reliability and efficiency of the existing spectral methods for isomorphism detection. ASME J. Mech. Des. 128 6 (2006) 1246-1252
36. Rao A.C. Genetic algorithm for characteristics of kinematic chains. ASME J. Mech. Des. 122 2 (2000) 228-231
37. Kong F.G., Li Q., and Zhang W.J. An artificial neural network approach to mechanism kinematic chain isomorphism identification. Mech. Mach. Theory 34 2 (1999) 271-283
38. Mruthyunjaya T.S. Kinematic structure of mechanisms revisited. Mech. Mach. Theory 38 4 (2003) 279-320
39. Ding H.F., and Huang Z. A unique representation of the kinematic chain and the atlas database. Mech. Mach. Theory 42 6 (2007) 637-651
40. Ding H.F., and Huang Z. A new theory for the topological structure analysis of kinematic chains and its applications. Mech. Mach. Theory 42 10 (2007) 1264-1279