Abstract
We formalize design patterns, commonly used in self-stabilization, to obtain general statements regarding both correctness and time complexity. Precisely, we study a class of algorithms devoted to networks endowed with a sense of direction describing a spanning forest whose characterization is a simple (i.e., quasi-syntactic) condition. We show that any algorithm of this class is (1) silent and self-stabilizing under the distributed unfair daemon, and (2) has a stabilization time polynomial in moves and asymptotically optimal in rounds. To illustrate the versatility of our method, we review several works where our results apply.
This study has been partially supported by the ANR projects DESCARTES (ANR-16-CE40-0023) and ESTATE (ANR-16-CE25-0009), and by the Franco-German DFG-ANR project 40300781 DISCMAT.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The level of p in G is the distance from p to the root of its tree in G (0 if p is the root itself).
- 2.
The height of \(A_i\) in \(\mathbf {GC}\) is 0 if the in-degree of \(A_i\) in \(\mathbf {GC}\) is 0. Otherwise, it is equal to one plus the maximum of the heights of the \(A_i\)’s predecessors w.r.t. \(\prec _{\mathcal {A}}\).
References
Altisen, K., Cournier, A., Devismes, S., Durand, A., Petit, F.: Self-stabilizing leader election in polynomial steps. Inf. Comput. 254, 330–366 (2017)
Arora, A., Gouda, M., Herman, T.: Composite routing protocols. In: SPDP 1990, pp. 70–78 (1990)
Blin, L., Fraigniaud, P., Patt-Shamir, B.: On proof-labeling schemes versus silent self-stabilizing algorithms. In: Felber, P., Garg, V. (eds.) SSS 2014. LNCS, vol. 8756, pp. 18–32. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11764-5_2
Blin, L., Potop-Butucaru, M.G., Rovedakis, S., Tixeuil, S.: Loop-free super-stabilizing spanning tree construction. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds.) SSS 2010. LNCS, vol. 6366, pp. 50–64. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16023-3_7
Blin, L., Tixeuil, S.: Compact deterministic self-stabilizing leader election on a ring: the exponential advantage of being talkative. Dist. Comp. 31(2), 139–166 (2018)
Chaudhuri, P.: An \(O(n^2)\) self-stabilizing algorithm for computing bridge-connected components. Computing 62(1), 55–67 (1999)
Chaudhuri, P.: A note on self-stabilizing articulation point detection. J. Syst. Arch. 45(14), 1249–1252 (1999)
Chaudhuri, P., Thompson, H.: Self-stabilizing tree ranking. Int. J. Comput. Math. 82(5), 529–539 (2005)
Chaudhuri, P., Thompson, H.: Improved self-stabilizing algorithms for l(2, 1)-labeling tree networks. Math. Comput. Sci. 5(1), 27–39 (2011)
Cournier, A., Devismes, S., Villain, V.: Light enabling snap-stabilization of fundamental protocols. TAAS 4(1), 6:1–6:27 (2009)
Datta, A.K., Devismes, S., Heurtefeux, K., Larmore, L.L., Rivierre, Y.: Competitive self-stabilizing \(k\)-clustering. TCS 626, 110–133 (2016)
Datta, A.K., Larmore, L.L., Vemula, P.: An \({O}({N})\)-time self-stabilizing leader election algorithm. JPDC 71(11), 1532–1544 (2011)
Delaët, S., Ducourthial, B., Tixeuil, S.: Self-stabilization with r-operators revisited. JACIC 3(10), 498–514 (2006)
Devismes, S.: A silent self-stabilizing algorithm for finding cut-nodes and bridges. Parallel Process. Lett. 15(1–2), 183–198 (2005)
Devismes, S., Ilcinkas, D., Johnen, C.: Silent self-stabilizing scheme for spanning-tree-like constructions. Technical report, HAL (2018)
Devismes, S., Johnen, C.: Silent self-stabilizing BFS tree algorithms revisited. JPDC 97, 11–23 (2016)
Dolev, S., Gouda, M.G., Schneider, M.: Memory requirements for silent stabilization. Acta Inf. 36(6), 447–462 (1999)
Ducourthial, B., Tixeuil, S.: Self-stabilization with r-operators. Dist. Comp. 14(3), 147–162 (2001)
Ghosh, S., Karaata, M.H.: A self-stabilizing algorithm for coloring planar graphs. Dist. Comp. 7(1), 55–59 (1993)
Christian, G., Nicolas, H., David, I., Colette, J.: Disconnected components detection and rooted shortest-path tree maintenance in networks. In: Felber, P., Garg, V. (eds.) SSS 2014. LNCS, vol. 8756, pp. 120–134. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11764-5_9
Huang, S.-T., Chen, N.-S.: A self-stabilizing algorithm for constructing breadth-first trees. IPL 41(2), 109–117 (1992)
Karaata, M.H.: A self-stabilizing algorithm for finding articulation points. Int. J. Found. Comput. Sci. 10(1), 33–46 (1999)
Katz, S., Perry, K.J.: Self-stabilizing extensions for message-passing systems. Dist. Comp. 7(1), 17–26 (1993)
Korman, A., Kutten, S., Peleg, D.: Proof labeling schemes. Dist. Comp. 22(4), 215–233 (2010)
Tel, G.: Introduction to Distributed Algorithms, 2nd edn. Cambridge University Press, Cambridge (2001)
Turau, V., Köhler, S.: A distributed algorithm for minimum distance-k domination in trees. J. Graph Algorithms Appl. 19(1), 223–242 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Altisen, K., Devismes, S., Durand, A. (2018). Acyclic Strategy for Silent Self-stabilization in Spanning Forests. In: Izumi, T., Kuznetsov, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2018. Lecture Notes in Computer Science(), vol 11201. Springer, Cham. https://doi.org/10.1007/978-3-030-03232-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-03232-6_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-03231-9
Online ISBN: 978-3-030-03232-6
eBook Packages: Computer ScienceComputer Science (R0)