Sense of direction: Definitions, properties, and classes

Networks

Volumn 32, Issue 3, 1998, Pages 165-180

  Flocchini, Paola ^a   Mans, Bernard ^b   Santoro, Nicola ^c  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b MACQUARIE UNIVERSITY   (Australia)

^c CARLETON UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039394291     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0037(199810)32:3<165::AID-NET1>3.0.CO;2-I     Document Type: Article

References (54)

1. D. Angluin, Local and global properties in networks of processors. Proceedings of 12th A.C.M. Symposium on Theory of Computing (1980) 82-93.
2. H. Attiya, M. Snir, and M. K. Warmuth, Computing on an anonymous ring. J. A.C.M. 35 (1988) 845-875.
3. H. Attiya, J. van Leeuwen, N. Santoro, and S. Zaks, Efficient elections in chordal ring networks. Algorithmica 4 (1989) 437-446.
4. P. W. Beame and H. L. Bodlaender, Distributed computing on transitive networks: The torus. Proceedings of 6th Symposium on Theoretical Aspects of Computer Science (1989) 294-303.
5. J.-C. Bermond, F. Comellas, and D. F. Hsu, Distributed loop computer networks: A survey. J. Parallel Distrib. Comput. 24 (1995) 2-10.
6. H. L. Bodlaender, New lower bound techniques for distributed leader finding and other problems on rings of processors. Theor. Comput. Sci. 81 (1991) 237-256.
7. F. T. Boesch and R. Tindell, Circulants and their connectivity. J. Graph Theory 8 (1984) 487-499.
8. P. Boldi and S. Vigna, Sense of direction and decision problems for Cayley graphs. Info. Process. Lett., to appear.
9. P. Boldi and S. Vigna, On the complexity of deciding sense of direction. Proceedings of the 2nd Colloquium on Structural Information and Communication Complexity, Olympia (1995) 39-52.
10. S. Dobrev and P. Ruzicka, Linear broadcasting and n log log n election in unoriented hypercubes. Proceedings of the 4th International Colloquium on Structural Information and Communication Complexity, Ascona (1997) 53-68.
11. P. Flocchini, Minimal sense of direction in regular networks. Info. Process. Lett. 61 (1997) 331-338.
12. P. Flocchini and B. Mans, Optimal election in labeled hypercubes. J. Parallel Distrib. Comput. 33 (1996) 76-83.
13. P. Flocchini, B. Mans, and N. Santoro, On the impact of sense of direction on message complexity. Info. Process. Lett. 63 (1997) 23-31.
14. P. Flocchini, A. Roncato, and N Santoro, Computing on anonymous networks with sense of direction. Theoretical Computer Science, to appear. (1996). Preliminary version in Proceedings of the 3rd Colloquium on Structural Information and Communication Complexity (1996) 32-46.
15. P. Flocchini, A. Roncato, and N. Santoro Symmetries and sense of direction in labeled graphs. Discrete Applied Mathematics, to appear. Preliminary version in Proceeding of the 27th SE Conference or Combinatorics, Graph Theory and Computing, Congress. Num. 121 (1996) 3-18.
16. P. Flocchini and N. Santoro, Topological constraints for sense of direction. Int. J. Found. Comput. Sci., to appear. Preliminary version in Proceedings of the 2nd Colloquium on Structural Information and Communication Complexity (1995) 27-38.
17. R. G. Gallager, P. A. Humblet, and P. M. Spira, A distributed algorithm for minimum spanning tree. A.C.M. Trans. Program. Lang. Syst. 5 (1983) 66-77.
18. Z. Harpaz and S. Zaks, Sense of direction in complete distributed networks. Technical Report TR-453, Department of Computer Science, Technion, Haifa 32000, Israel (April 1987). Extended abstract in the Proceedings of the 23rd Allerton Conference on Communication, Control and Computing (October 1985).
19. A. Israeli and M. Jalfon, Uniform self-stabilizing ring orientation. Info. Comput. 104 (1993) 175-196.
20. A. Israeli, E. Kranakis, D. Krizanc, and N. Santoro, Time-message trade-offs for the weak unison problem. Conference on Algorithms and Complexity Rome (1994). Lecture Notes in Computer Science 778. Springer-Verlag, 167-178.
21. T. Z. Kalamboukis and S. L. Mantzaris, Towards optimal distributed election on chordal rings. Info. Process. Lett. 38 (1991) 265-270.
22. E. Korach, S. Moran, and S. Zaks, Tight lower and upper bounds for a class of distributed algorithms for a complete network of processors. Proceedings of the 3rd Symposium on Principles of Distributed Computing, Vancouver, (1984) 199-207.
23. E. Kranakis and D. Krizanc, Labeled versus unlabeled distributed Cayley networks. Discr. Appl. Math. 63 (1995) 223-236.
24. E. Kranakis and D. Krizanc, Distributed computing on anonymous hypercubes. J. Alg. 23 (1997) 32-50.
25. E. Kranakis, D. Krizanc, and J. van den Berg, Computing Boolean functions on anonymous networks. Proceedings of the 17th International Colloquium on Automata, Languages, and Programming (1990). Lecture Notes in Computer Science 443. Springer-Verlag, 254-267.
26. E. Kranakis and N. Santoro. Distributed computing on anonymous hypercubes with faulty components. Proceedings of the 6th International Workshop of Distributed Algorithms (1992). Lecture Notes in Computer Science 647. Springer-Verlag, 253-263.
27. I. Lavallée and G. Roucairol, A fully distributed (minimal) spanning tree algorithm. Info. Process. Lett. 23 (1986) 55-62.
28. M. C. Loui, T. A. Matsushita, and D. B. West, Election in complete networks with a sense of direction. Info. Process. Lett. 22 (1986) 185-187. See also Info. Process. Lett. 28 (1988) 327.
29. M. C. Loui, T. A. Matsushita, and D. B. West, Election in complete networks with a sense of direction. Info. Process. Lett. 22 (1986) 185-187. See also Info. Process. Lett. 28 (1988) 327.
30. B. Mans, Optimal distributed algorithms in unlabeled tori and chordal rings. J. Parallel Distrib. Comput., to appear. Preliminary version in Proceedings of the 3rd International Colloquium on Structural Information and Communication Complexity (1996) 17-31.
31. B. Mans and N. Santoro, Optimal fault-tolerant leader election in chordal rings. IEEE Trans. Comput., to appear.
32. B. Mans and N. Santoro, On the impact of sense of direction in arbitrary networks. Proceedings of the 14th International Conference on Distributed Computing Systems, Poznan (1994) 258-265.
33. S. L. Mantzaris, Almost optimal election in chordal rings. Proceedings of the Conference on Parallel and Distributed Computing in Engineering Systems (1991) 459-464.
34. G. H. Masapati and H. Ural, Effect of preprocessing on election in a complete network with a sense of direction. Proceedings of the I.E.E.E. International Conference on Systems, Man and Cybernetics 3 (1991) 1627-1632.
35. T. Masuzawa, N. Nishikawa, K. Hagihara, and N. Tokura, Optimal fault-tolerant distributed algorithms for election in complete networks with a global sense of direction. Proceedings of the 3rd International Workshop on Distributed Algorithms (1989). Lecture Notes in Computer Science 392. Springer-Verlag, 171-182.
36. T. Masuzawa, N. Nishikawa, K. Hagihara, and N. Tokura, A fault-tolerant algorithm for election in complete networks with a sense of direction. Syst. Comput. Jpn. 22(12) (1991) 11-22.
37. N. Norris, Classifying anonymous networks: When can two networks compute the same vector-valued functions? Proceedings of the 1st Colloquium on Structural Information and Communication Complexity, Ottawa (1994) 83-98.
38. Y. Pan, An improved election algorithm in chordal ring networks. Int. J. Comput. Math. 40(3-4) (1991), 191-200.
39. Y. Pan, A near-optimal multi-stage distributed algorithm for finding leaders in clustered chordal rings. Info. Sci. 76(1-2) (1994) 131-140.
40. G. L. Peterson, Efficient algorithms for elections in meshes and complete networks. Technical Report TR-140, Dept. of Computer Science, University of Rochester, Rochester, NY 14627 (1985).
41. S. Robbins and K. A. Robbins, Choosing a leader on a hypercube. Proceedings of the International Conference on Databases, Parallel Architectures and their Applications, Miami Beach (1990) 469-471.
42. N. Santoro, On the message complexity of distributed problems. J. Comput. Info. Sci. 13 (1984) 131-147.
43. N. Santoro, Sense of direction, topological awareness and communication complexity. SIGACT NEWS 2(16) (1984) 50-56.
44. N. Santoro, J. Urrutia, and S. Zaks, Sense of direction and communication complexity in distributed networks. Proceedings of the 1st International Workshop on Distributed Algorithms, Ottawa (1985). Carleton University Press, 123-132.
45. M. B. Sharma, S. S. Iyengar, and N. K. Mandyam, An efficient distributed depth-first-search algorithm. Info. Process. Lett. 32 (1989) 183-186. See also Info. Process. Lett. 35 (1990) 55.
46. M. B. Sharma, S. S. Iyengar, and N. K. Mandyam, An efficient distributed depth-first-search algorithm. Info. Process. Lett. 32 (1989) 183-186. See also Info. Process. Lett. 35 (1990) 55.
47. G. Singh, Efficient leader election using sense of direction. Distrib. Comput. 10 (1997) 159-165.
48. V. Syrotiuk and J. Pachl, A distributed ring orientation algorithm. Proceedings of the 2nd International Workshop on Distributed Algorithms, Amsterdam (1987). Lecture Notes in Computer Science 312. Springer-Verlag, 332-336.
49. G. Tel, Network orientation. Int. J. Found. Comput. Sci. 5 (1994) 1-41.
50. G. Tel, Linear election in hypercubes. Parallel Process. Lett. 5 (1995) 357-366.
51. G. Tel, Sense of direction in processor networks. Proceedings of the Conference on Theory and Practice of Informatics (1995). Lecture Notes in Computer Science 1012. Springer-Verlag, 50-82.
52. J. van Leeuwen and R. Tan, Compact routing: A survey. Proceedings of the 1st Colloquium on Structural Information and Communication Complexity, Ottawa (1994) 99-110.
53. A. M. Verweij, Linear-message election in hypercubes. Manuscript.
54. M. Yamashita and T. Kameda, Computing on anonymous networks, Part I: Characterizing the solvable cases. IEEE Trans. Parallel Distrib. Comput. 7 (1996) 69-89.