. Il-existe-un-suffixe-infini-e-de-e-o, egles de B sont activables mais seules des r` egles de Reset(B) sont exécutées. Alors, des r` egles de Reset(B) sont exécutées infiniment souvent dans e . Or, d'après la propriété 6.2.1 (point 1), chaque cycle de calcul de Reset(B) est exécuté en un nombre fini de mouvements. Donc, Reset(B) exécute des cycles de calcul infiniment souvent dans e . D'après l'hypothèse 6.3.1, les variables de Reset(B) se comportent dans e comme le protocole PIR qui est instantanément stabilisant d'après le théorème 6.2.1. Donc, durant le premier cycle complet de calcul dans e , Reset(B) exécute, en particulier, une phase de retourcompì ete. Or, quand r exécute sa phase de retour (r` egle F ck), r réinitialise ses variables de B en utilisant B, Status p i = C) ? ¬Bad

?. Supposons-que, T. , =. F. Si, T. , =. F. et al., (p) par l'exécution de r` egles New et F wd jusqu'` a ce que Status p = F . Après que p ait exécuté ces deux r` egles, Status p = F et nous retrouvons le cas 1. Si T race- Status(CheminBF S(p)) = F + B + , alors p n'est plus activable tant que Status Pp = R. Or, ?p ? CheminBF S(p), p = r ? Status p = R et r est le seul processeur

?. Supposons-que, T. , and =. , Dans ce cas, la valeur R descend dans CheminBF S(p) jusqu'` a ce que Status p = R, Donc, p exécute au plus une r` egle New avant de vérifier le cas 2

D. 'o-`-u, S. Q. , and =. , alors p peut au plus exécuter trois r` egles avant d'exécuter la r` egle D ou la r` egle Err. b) q = r. Dans ce cas, d'après la définition 6

?. Sinon and . Dans-le, pire des cas, p participè a D ?k phasescompì etes o` u k est la distance de p ` a r dans ArbreBF S r . Or, ` a chaque phasecompì ete o` u p participe, p exécute une r` egle New, une r` egle F wd et une r` egle Bck. Donc, si p = r

D. 'o-`-u, ?. Tel-que-status-p, ?. {r, and F. B}, (D) r` egles avant d'exécuter Status p := D, p.p exécute O

. Preuve and . Supposons, End(r) n'est pas vérifié. Par contradiction, Status r = D dans ? (cf. définition de BF S.End(r) dans l'algorithme 6.4.21) et ?p ? V , p vérifie ¬Error(p) (sinon, la r` egle Err de p est activable) NousétudionsNous´Nousétudions alors la configuration ? en fonction de ces deux cas : 1. Status r = C dans ?. Comme nous avons ¬Error(r), r vérifie Start(r)

=. Status-r, ?. Dans-?-?p, S. Arbrebf, and S. (. Race-statuscheminbf, Soit p ? ArbreBF S r . a) Supposons que p = r, Status p = B, et Status Pp = R dans ?. Alors, ?q ? Children p , Status q ? {B,D} car q = r ? ¬Error(q) et la r` egle New de p est activable. Ainsi, ? n'est pas une configuration terminale, contradiction. b) Supposons que p = r

?. Si-?q-?-children-p, Status q = B alors, d'après a), la r` egle New de q est activable et ? n'est pas une configuration terminale, contradiction

?. Sinon, S. Children-p, ?. {r, and . D}-et-la-r-`-egle-f-wd-de-p-est-activable, est pas une configuration terminale, contradiction. c) Supposons que Status p = F dans ?. Sans perte de généralité, nous supposons que p vérifie Level p = max({Level q :: q ? ArbreBF S r ? Status q = F }) Alors, ?q ? Children p , Status q ? {R,B,D} car q = r ?¬Error(q) Si ?q ? Children p , Status q = R, alors, d'après b), q est activable dans ? et ? n'est pas une configuration terminale, contradiction. Donc, ?q ? Children p , Status q ? {B,D}. ? Supposons que ?p ? Neig p , Status p = C

?. ¬error, p vérifie Leaf (p ) et sa r` egle Hk est activable. Ainsi, ? n'est pas une configuration terminale, contradiction

C. ?p, ?. Children-r, S. , and ?. {r, D} (n.b. ?p ? Children r , p = r ? ¬Error(p)), r vérifie aussi ROk(r) et la r` egle F

D. Ainsi and S. E. Status-r-=-d-i, End(r) n'est pas satisfait, alors ? n'est pas une configuration terminale

[. Bibliographie, G. Afek, and . Brown, Self-stabilization over unreliable communication media, Distributed Computing, vol.7, pp.27-34, 1993.

[. Afek and A. Bremler, Self-stabilizing unidirectional network algorithms by power supply, Chicago Journal of Theoretical Computer Science, issue.3, 1998.

[. Awerbuch and R. Gallager, Distributed BFS algorithms, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985), pp.250-256, 1985.
DOI : 10.1109/SFCS.1985.20

[. Arora and M. Gouda, Distributed reset, IEEE Transactions on Computers, vol.43, issue.9, pp.1026-1038, 1994.
DOI : 10.1109/12.312126

A. Ahmad, Simple enumeration of minimal cutsets of acyclic directed graph, IEEE Transactions on Reliability, vol.37, issue.5, pp.484-487, 1988.
DOI : 10.1109/24.9868

[. Aggarwal and S. Kutten, Time optimal self-stabilizing spanning tree algorithms, FSTTCS'93, pp.400-410, 1993.
DOI : 10.1007/3-540-57529-4_72

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.5742

. Awerbuch, Y. Kutten, . Mansour, G. Patt-shamir, and . Varghese, Time optimal selfstabilizing synchronization, STOC93 Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pp.652-661, 1993.

Y. Afek, M. Kutten, and . Yung, Memory-efficient self-stabilization on general networks, WDAG90 Distributed Algorithms 4th International Workshop Proceedings, pp.486-501, 1990.

B. Awerbuch, G. Patt-shamir, and . Varghese, Self-stabilization by local checking and correction, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science, pp.268-277, 1991.
DOI : 10.1109/SFCS.1991.185378

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.211.8704

J. [. Aho and . Ullman, Concept fondamentaux de l'informatique. Dunod, 1992.

B. Awerbuch, Complexity of network synchronization, Journal of the ACM, vol.32, issue.4, pp.804-823, 1985.
DOI : 10.1145/4221.4227

B. Awerbuch, A new distributed Depth-First-Search algorithm, Information Processing Letters, vol.20, issue.3, pp.147-150, 1985.
DOI : 10.1016/0020-0190(85)90083-3

[. Ahuja and Y. Zhu, An efficient distributed algorithm for finding articulation points, Bridges, and biconnected components in asynchronous networks, 9th Conference on Foundations of Software Technology and Theorical Computer Science, pp.99-108, 1989.
DOI : 10.1007/3-540-52048-1_36

[. Beauquier and B. Bérard, Systèmes d'exploitation, 1990.

[. Blin, V. Cournier, and . Villain, An Improved Snap-Stabilizing PIF Algorithm, DSN SSS'03 Workshop : Sixth Symposium on Self-Stabilizing Systems (SSS'03), pp.199-214, 2003.
DOI : 10.1007/3-540-45032-7_15

URL : https://hal.archives-ouvertes.fr/hal-01310823

A. Bui, . Datta, V. Petit, and . Villain, Snap-stabilizing PIF algorithm in tree networks without sense of direction, SIROCCO'99, The 6th International Colloquium On Structural Information and Communication Complexity Proceedings, pp.32-46, 1999.

A. Bui, . Datta, V. Petit, and . Villain, Space optimal PIF algorithm: self-stabilized with no extra space, 1999 IEEE International Performance, Computing and Communications Conference (Cat. No.99CH36305), pp.20-26, 1999.
DOI : 10.1109/PCCC.1999.749416

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.5137

A. Bui, . Datta, V. Petit, . Bein, V. Datta et al., State-optimal snap-stabilizing PIF in tree networks Snap-stabilizing optimal binary search tree, Proceedings of the Fourth Workshop on Self-Stabilizing Systems Seventh International Symposium on Self-Stabilizing Systems (SSS'05) 2005. LNCS 3764. [Ber83] C Berge. Graphes et hypergraphes. BordasCD94] Z Collin and S Dolev. Self-stabilizing depth-first search. Information Processing Letters, pp.78-85, 1983.

A. Cournier, . Datta, V. Petit, and . Villain, Optimal snap-stabilizing PIF in unoriented trees, OPODIS 2001, Fifth International Conference On Principles Of Distributed Systems, 2001.

A. Cournier, . Datta, V. Petit, and . Villain, Self-stabilizing PIF algorithm in arbitrary rooted networks, Proceedings 21st International Conference on Distributed Computing Systems, pp.91-98, 2001.
DOI : 10.1109/ICDSC.2001.918937

A. Cournier, . Datta, V. Petit, and . Villain, Snap-stabilizing PIF algorithm in arbitrary rooted networks, 22st International Conference on Distributed Computing Systems (ICDCS-22), pp.199-206, 2002.

A. Cournier, . Datta, V. Petit, and . Villain, Enabling snap-stabilization, 23rd International Conference on Distributed Computing Systems, 2003. Proceedings., pp.12-19, 2003.
DOI : 10.1109/ICDCS.2003.1203447

A. Cournier, . Devismes, V. Petit, and . Villain, Snap-Stabilizing Depth-First Search on Arbitrary Networks, OPODIS'04, International Conference On Principles Of Distributed Systems Proceedings, pp.267-282, 2004.
DOI : 10.1093/comjnl/bxh154

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.3661

A. Cournier, . Devismes, V. Petit, and . Villain, Snap-Stabilizing Depth-First Search on Arbitrary Networks, The Computer Journal, vol.49, issue.3, pp.268-280, 2006.
DOI : 10.1093/comjnl/bxh154

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.3661

A. Cournier, V. Devismes, and . Villain, Snap-Stabilizing Detection of Cutsets, HIPC 2005, 12th Annual IEEE Conference on High Performance Computing, pp.488-497, 2005.
DOI : 10.1007/11602569_50

A. Cournier, V. Devismes, and . Villain, A Snap-Stabilizing DFS with a Lower Space Requirement, Seventh International Symposium on Self-Stabilizing Systems (SSS'05), pp.33-47, 2005.
DOI : 10.1007/11577327_3

A. Cournier, V. Devismes, and . Villain, From Self- to Snap- Stabilization, 8th International Symposium on Self-Stabilization, Safety, and Security (SSS'06), pp.199-213, 2006.
DOI : 10.1007/978-3-540-49823-0_14

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.1939

A. Cournier, V. Devismes, and . Villain, Snap-stabilizing PIF and useless computations, 12th International Conference on Parallel and Distributed Systems, (ICPADS'06), pp.39-46, 2006.
DOI : 10.1109/ICPADS.2006.100

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.726

[. Cournier, V. Devismes, and . Villain, Snap-stabilizing PIF and useless computations, 12th International Conference on Parallel and Distributed Systems, (ICPADS'06), 2006.
DOI : 10.1109/ICPADS.2006.100

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.726

[. Chang, Echo Algorithms: Depth Parallel Operations on General Graphs, IEEE Transactions on Software Engineering, vol.8, issue.4, pp.391-401, 1982.
DOI : 10.1109/TSE.1982.235573

[. Chaudhuri, A note on self-stabilizing articulation point detection, Journal of Systems Architecture, vol.45, issue.14, pp.1249-1252, 1999.
DOI : 10.1016/S1383-7621(98)00062-9

[. Chaudhuri, An $O(n^2)$ Self-Stabilizing Algorithm for Computing Bridge-Connected Components, Computing, vol.62, issue.1, pp.55-67, 1999.
DOI : 10.1007/s006070050013

[. Cidon, Yet another distributed depth-first-search algorithm, Information Processing Letters, vol.26, issue.6, pp.301-305, 1988.
DOI : 10.1016/0020-0190(88)90187-1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.8498

J. [. Chandy and . Misra, Distributed computation on graphs: shortest path algorithms, Communications of the ACM, vol.25, issue.11, 1982.
DOI : 10.1145/358690.358717

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.104.8179

J. [. Chandy, L. M. Misra, and . Haas, Distributed deadlock detection, ACM Transactions on Computer Systems, vol.1, issue.2, pp.144-156, 1983.
DOI : 10.1145/357360.357365

[. Cournier, One dollar questions. Preliminary work, 2002.

[. Chang and R. Roberts, An improved algorithm for decentralized extrema-finding in circular configurations of processes, Communications of the ACM, vol.22, issue.5, pp.281-283, 1979.
DOI : 10.1145/359104.359108

[. Chandra and S. Toueg, Unreliable failure detectors for asynchronous systems, PODC91, The Tenth Annual ACM Symposium on Principles of Distributed Computing, pp.325-340, 1991.
DOI : 10.1145/112600.112627

[. Chen, S. Yu, and . Huang, A self-stabilizing algorithm for constructing spanning trees, Information Processing Letters, vol.39, issue.3, pp.147-151, 1991.
DOI : 10.1016/0020-0190(91)90111-T

[. Devismes, A silent self-stabilizing algorithm for finding cut-nodes and bridges. Parallel Processing Letters, pp.183-198, 2005.

A. Kumar-datta, S. Gurumurthy, F. Petit, and V. Villain, Selfstabilizing network orientation algorithms in arbitrary rooted networks, International Conference on Distributed Computing Systems, pp.576-583, 2000.

. [. Dolev, M. Gouda, and . Schneider, Memory requirements for silent stabilization, PODC96 Proceedings of the Fifteenth Annual ACM Symposium on Principles of Distributed Computing, pp.27-34, 1996.

]. E. Dij65 and . Dijkstra, Solution of a problem in concurrent programming control, Communications of the ACM, vol.8, issue.9, p.569, 1965.

[. Dijkstra, Self-stabilizing systems in spite of distributed control, Communications of the Association of the Computing Machinery, pp.643-644, 1974.
DOI : 10.1145/361179.361202

[. Dolev, S. Israeli, and . Moran, Resource bounds for self stabilizing message driven protocols, PODC91, the tenth annual ACM symposium on Principles Of Distributed Computing, pp.281-293, 1991.
DOI : 10.1137/s0097539792235074

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.9936

[. Dolev, S. Israeli, and . Moran, Self-stabilization of dynamic systems assuming only read/write atomicity, Distributed Computing, pp.3-16, 1993.
DOI : 10.1007/BF02278851

[. Dolev, S. Israeli, and . Moran, Uniform dynamic self-stabilizing leader election, IEEE Transactions on Parallel and Distributed Systems, vol.8, issue.4, pp.424-440, 1997.
DOI : 10.1109/71.588622

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.7453

A. Datta, C. Johnen, V. Petit, E. W. Villain, C. S. Dijkstra et al., Termination detection from diffusing computations [DT01] B Ducourthial and S Tixeuil. Self-stabilization with r-operators. Distributed Computing Two-state self-stabilizing algorithms for token rings Cutset enumeration of network systems with link and node failure Impossibility of distributed consensus with one faulty process, Self-stabilizing depth-first token circulation in arbitrary rooted networks. Distributed Computing, pp.207-2181, 1980.

S. Ghosh, . Gupta, S. Herman, . G. Pemmaraju-[-ghs83-]-r, P. A. Gallager et al., Fault-containing self-stabilizing distributed protocols A distributed algorithm for minimum weight spanning trees A self-stabilizing algorithm for constructing breadth-first trees, Self-stabilizing depth-first token circulation on networks. Distributed Computing, pp.67-77109, 1983.

T. Herman, Binary self-stabilization in distributed systems Self-stabilization : ramdomness to reduce space, Information Processing Letters Information Processing Letters, vol.40, issue.6, pp.153-15995, 1991.

C. Johnen, C. Alari, A. Beauquier, and . Datta, Self-stabilizing depth-first token passing on rooted networks, WDAG97 Distributed Algorithms 11th International Workshop Proceedings, Springer-Verlag LNCS :1320, pp.260-274, 1997.
DOI : 10.1007/BFb0030689

C. Johnen, L. Alima, A. K. Datta, and S. Tixeuil, OPTIMAL SNAP-STABILIZING NEIGHBORHOOD SYNCHRONIZER IN TREE NETWORKS, Parallel Processing Letters, vol.12, issue.03n04, pp.327-340, 2002.
DOI : 10.1142/S0129626402001026

C. Johnen and J. Beauquier, Space-efficient distributed self-stabilizing depthfirst token circulation Memory efficient, self-stabilizing algorithm to construct BFS spanning trees, Proceedings of the Second Workshop on Self-Stabilizing Systems PODC97 Proceedings of the Sixteenth Annual ACM Symposium on Principles of Distributed Computing, pp.4-5, 1995.
DOI : 10.1145/259380.259508

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.1830

J. Jaffar, A. E. Santosa, R. H. Yap, and K. Q. Zhu, Scalable distributed depth-first search with greedy work stealing, 16th IEEE International Conference on Tools with Artificial Intelligence, pp.98-103, 2004.
DOI : 10.1109/ICTAI.2004.107

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.7497

[. Karaata, A SELF-STABILIZING ALGORITHM FOR FINDING ARTICULATION POINTS, International Journal of Foundations of Computer Science, vol.10, issue.01, pp.33-46, 1999.
DOI : 10.1142/S0129054199000046

[. Karger, Minimum cuts in near-linear time, Journal of the ACM, vol.47, issue.1, pp.46-76, 2000.
DOI : 10.1145/331605.331608

M. Hakan, K. , and P. Chaudhuri, A self-stabilizing algorithm for bridge finding, Distributed Computing, pp.47-53, 1999.

[. Katz and K. Perry, Self-stabilizing extensions for message-passing systems, Proceedings of the ninth annual ACM symposium on Principles of distributed computing , PODC '90, pp.17-26, 1993.
DOI : 10.1145/93385.93405

[. Kruijer, Self-stabilization (in spite of distributed control) in tree-structured systems, Information Processing Letters, vol.8, issue.2, pp.91-95, 1979.
DOI : 10.1016/0020-0190(79)90151-0

]. L. Lam78 and . Lamport, Time, clocks, and the ordering of events in a distributed system, Communications of the ACM, vol.21, issue.7, pp.558-564, 1978.

[. Lann, Distributed systems : towards a formal approach, Information Proces- sing'77, pp.155-160, 1977.

T. [. Lai and . Yang, On distributed snapshots, Information Processing Letters, vol.25, issue.3, pp.153-158, 1987.
DOI : 10.1016/0020-0190(87)90125-6

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.5518

[. Lynch, Distributed algorithms, 1996.

]. F. Mat87 and . Mattern, Algorithms for distributed termination detection, Distributed Computing, pp.161-175, 1987.

[. Mattern, Virtual time and global states of distributed systems, Proceedings of International Workshop on Parallel and Distributed System, pp.215-226, 1988.

R. [. Menasce and . Muntz, Locking and deadlock detection in distributed databases, Communications of the ACM, vol.21, 1979.

M. [. Mitchell and . Merritt, A distributed algorithm for deadlock detection and resolution, Proceedings of the third annual ACM symposium on Principles of distributed computing , PODC '84, pp.215-226, 1988.
DOI : 10.1145/800222.806755

Y. [. Moran and . Wolfstahl, Extended impossibility results for asynchronous complete networks, Information Processing Letters, vol.26, issue.3, pp.145-151, 1987.
DOI : 10.1016/0020-0190(87)90052-4

D. [. Nellari, S. C. Maric, S. Farantos, and . Stamatiadis, Report on grid enabling technologies in the context of the enacts collaboration, 2002.

F. Nolot, Stabilisation des horloges de phases dans les systèmessyst`systèmes distribués, 2002.

M. [. Naimi and . Trehel, How to detect and regenerate the token in the log(N) distributed algorithm for mutual exclusion, Proceedings of 7th IEEE International Conference on Distributed Computing Systems, pp.371-375, 1987.

K. Paton, An algorithm for the blocks and cutnodes of a graph, Communications of the ACM, vol.14, issue.7, pp.468-475, 1971.
DOI : 10.1145/362619.362628

J. Provan and M. Ball, The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected, SIAM Journal on Computing, vol.12, issue.4, pp.777-788, 1983.
DOI : 10.1137/0212053

F. Petit, Efficacité et simplicité dans les algorithmes distribués auto-stabilisants de parcours en profondeur de jeton, 1998.

[. Petit, Fast Self-Stabilizing Depth-First Token Circulation, Proceedings of the Fifth Workshop on Self-Stabilizing Systems, Lisbonne (Portugal), pp.200-215, 2001.
DOI : 10.1007/3-540-45438-1_14

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.4623

L. Pilard, Observer la stabilisation, 2005.

J. Parks, . Tokura, K. Masuzawa, and . Hagihara, Efficient distributed algorithms solving problems about the connectivity of network, Systems and Computers in Japan, vol.1, issue.7, pp.1-16, 1991.
DOI : 10.1002/scj.4690220801

[. Petit and V. Villain, Color optimal self-stabilizing depth-first token circulation. In I-SPAN'97, Third International Symposium on Parallel Architectures, Algorithms and Networks Proceedings, pp.317-323, 1997.
DOI : 10.1109/ispan.1997.645114

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.3974

[. Petit and V. Villain, Time and space optimality of distributed depth-first token circulation algorithms, Proceedings of DIMACS Workshop on Distributed Data and Structures, pp.91-106, 1999.

[. Petit and V. Villain, Optimal snap-stabilizing depth-first token circulation in tree networks, Journal of Parallel and Distributed Computing, vol.67, issue.1, 2003.
DOI : 10.1016/j.jpdc.2006.08.008

A. [. Ricart and . Agrawala, An optimal algorithm for mutual exclusion in computer networks, Communications of the ACM, vol.24, issue.1, pp.9-17, 1981.
DOI : 10.1145/358527.358537

[. Rai, A Cutset Approach to Reliability Evaluation in Communication Networks, IEEE Transactions on Reliability, vol.31, issue.5, pp.428-431, 1982.
DOI : 10.1109/TR.1982.5221415

. Seg83, Distributed network protocols, IEEE Transactions on Information Theory, IT, vol.29, pp.23-35, 1983.

[. Spraque and K. Kulkarni, Optimal parallel algorithms for finding cut vertices and bridges of interval graphs, Information Processing Letters, vol.42, issue.4, pp.229-234, 1992.
DOI : 10.1016/0020-0190(92)90244-P

[. Sur and P. Srimani, A self-stabilizing distributed algorithm to construct BFS spanning trees on a symetric graph. Parallel Processing Letters, pp.171-179, 1992.

[. Tajibnapis, A correctness proof of a topology information maintenance protocol for a distributed computer network, Communications of the ACM, vol.20, issue.7, pp.477-485, 1977.
DOI : 10.1145/359636.359701

E. Robert and . Tarjan, Depth-first search and linear graph algorithms, SIAM J. Computing, vol.1, issue.2, 1972.

G. Tel, Introduction to distributed algorithms, 2001.
DOI : 10.1017/CBO9781139168724

URL : http://dx.doi.org/10.1016/s0898-1221(97)90063-8

]. S. Tou80, I. T. Toueg, . Watson-research, and . Center, An all-pairs shortest-path distributed algorithm, 1980.

[. Varghese, Self-stabilization by local checking and correction, 1993.

R. B. Van-leeuwen and . Tan, Interval Routing, The Computer Journal, vol.30, issue.4, pp.298-307, 1987.
DOI : 10.1093/comjnl/30.4.298

[. Whited, D. Shier, and J. Jarvis, Reliability Computations for Planar Networks, ORSA Journal on Computing, vol.2, issue.1, pp.46-60, 1990.
DOI : 10.1287/ijoc.2.1.46