Document Open Access Logo

Self-Stabilizing Fully Adaptive Maximal Matching

Authors Shimon Bitton, Yuval Emek , Taisuke Izumi , Shay Kutten

PDF

File

Thumbnail PDF
PDF
LIPIcs.OPODIS.2024.33.pdf
  • Filesize: 0.91 MB
  • 21 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Computer systems organization → Fault-tolerant network topologies
Keywords
  • self-stabilization
  • maximal matching
  • fully adaptive run-time
  • dynamic graphs

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

A self-stabilizing randomized algorithm for mending maximal matching (MM) in synchronous networks is presented. Starting from a legal MM configuration and assuming that the network undergoes k faults or topology changes (that may occur in multiple batches), the algorithm is guaranteed to stabilize back to a legal MM configuration in time O(log k) in expectation and with high probability (in k), using constant size messages. The algorithm is simple to implement and is uniform in the sense that it does not assume unique identifiers, nor does it assume any global knowledge of the communication graph including its size. It relies on a generic probabilistic phase synchronization technique that may be useful for other self-stabilizing problems. The algorithm compares favorably with the existing self-stabilizing MM algorithms in terms of the dependence of its run-time on k, a.k.a. fully adaptive run-time. In fact, this dependence is asymptotically optimal for uniform algorithms that use constant size messages.

Cite As Get BibTex

Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Self-Stabilizing Fully Adaptive Maximal Matching. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2024.33

Author Details

Shimon Bitton
  • Intel Corporation, Haifa, Israel
Yuval Emek
  • Technion - Israel Institute of Technology, Haifa, Israel
Taisuke Izumi
  • Osaka Unversity, Japan
Shay Kutten
  • Technion - Israel Institute of Technology, Haifa, Israel

Funding

  • Emek, Yuval: supported by the Bernard M. Gordon Center for Systems Engineering at the Technion.
  • Izumi, Taisuke: supported by JSPS KAKENHI Grant Numbers 23H04385 and 22H03569.
  • Kutten, Shay: supported by ISF grant 1346/22 and by the Grand Technion Energy Program.

References

  1. Yehuda Afek and Shlomi Dolev. Local stabilizer. Journal of Parallel and Distributed Computing, 62(5):745-765, 2002. URL: https://doi.org/10.1006/jpdc.2001.1823.
  2. Yehuda Afek, Shay Kutten, and Moti Yung. The local detection paradigm and its applications to self-stabilization. Theoretical Computer Science, 186(1-2):199-229, 1997. URL: https://doi.org/10.1016/S0304-3975(96)00286-1.
  3. Noga Alon, László Babai, and Alon Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of algorithms, 7(4):567-583, 1986. URL: https://doi.org/10.1016/0196-6774(86)90019-2.
  4. Karine Altisen, Stéphane Devismes, Swan Dubois, and Franck Petit. Introduction to distributed self-stabilizing algorithms. Synthesis Lectures on Distributed Computing Theory, 8(1):1-165, 2019. URL: https://doi.org/10.2200/S00908ED1V01Y201903DCT015.
  5. Ozkan Arapoglu and Orhan Dagdeviren. An asynchronous self-stabilizing maximal independent set algorithm in wireless sensor networks using two-hop information. In 2019 International Symposium on Networks, Computers and Communications (ISNCC), pages 1-5. IEEE, 2019. URL: https://doi.org/10.1109/ISNCC.2019.8909189.
  6. Anish Arora and Hongwei Zhang. LSRP: Local stabilization in shortest path routing. IEEE/ACM Transactions on Networking, 14(3):520-531, 2006. URL: https://doi.org/10.1145/1143396.1143402.
  7. Yuma Asada, Fukuhito Ooshita, and Michiko Inoue. An efficient silent self-stabilizing 1-maximal matching algorithm in anonymous networks. Journal of Graph Algorithms and Applications, 20(1):59-78, 2016. URL: https://doi.org/10.7155/jgaa.00384.
  8. Baruch Awerbuch, Boaz Patt-Shamir, and George Varghese. Self-stabilization by local checking and correction (extended abstract). In 32nd Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 1-4 October 1991, pages 268-277. IEEE, IEEE Computer Society, 1991. URL: https://doi.org/10.1109/SFCS.1991.185378.
  9. Baruch Awerbuch, Boaz Patt-Shamir, George Varghese, and Shlomi Dolev. Self-stabilization by local checking and global reset (extended abstract). In Distributed Algorithms, 8th International Workshop, WDAG '94, Terschelling, The Netherlands, September 29 - October 1, 1994, Proceedings, volume 857, pages 326-339. Springer, Springer, 1994. URL: https://doi.org/10.1007/BFb0020443.
  10. Baruch Awerbuch and George Varghese. Distributed program checking: A paradigm for building self-stabilizing distributed protocols (extended abstract). In 32nd Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 1-4 October 1991, pages 258-267. IEEE, IEEE Computer Society, 1991. URL: https://doi.org/10.1109/SFCS.1991.185377.
  11. Yossi Azar, Shay Kutten, and Boaz Patt-Shamir. Distributed error confinement. In Proceedings of the twenty-second annual symposium on Principles of distributed computing, pages 33-42, 2003. URL: https://doi.org/10.1145/872035.872041.
  12. Alkida Balliu, Sebastian Brandt, Juho Hirvonen, Dennis Olivetti, Mikaël Rabie, and Jukka Suomela. Lower bounds for maximal matchings and maximal independent sets. In 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), pages 481-497. IEEE, 2019. URL: https://doi.org/10.1109/FOCS.2019.00037.
  13. Alkida Balliu, Juho Hirvonen, Darya Melnyk, Dennis Olivetti, Joel Rybicki, and Jukka Suomela. Local mending. In Merav Parter, editor, Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Paderborn, Germany, June 27-29, 2022, Proceedings, pages 1-20, 2022. URL: https://doi.org/10.1007/978-3-031-09993-9_1.
  14. Philipp Bamberger, Fabian Kuhn, and Yannic Maus. Local distributed algorithms in highly dynamic networks. In 2019 IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019, Rio de Janeiro, Brazil, May 20-24, 2019, pages 33-42, 2019. URL: https://doi.org/10.1109/IPDPS.2019.00015.
  15. Leonid Barenboim, Michael Elkin, and Uri Goldenberg. Locally-iterative distributed (Δ + 1)-coloring and applications. J. ACM, 69(1):5:1-5:26, 2022. URL: https://doi.org/10.1145/3486625.
  16. Leonid Barenboim, Michael Elkin, Seth Pettie, and Johannes Schneider. The locality of distributed symmetry breaking. J. ACM, 63(3):20:1-20:45, 2016. URL: https://doi.org/10.1145/2903137.
  17. Surender Baswana, Manoj Gupta, and Sandeep Sen. Fully dynamic maximal matching in O(log n) update time. SIAM Journal on Computing, 44(1):88-113, 2015. URL: https://doi.org/10.1137/130914140.
  18. Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Fully adaptive self-stabilizing transformer for LCL problems. CoRR, abs/2105.09756, 2024. URL: https://doi.org/10.48550/arXiv.2105.09756.
  19. Keren Censor-Hillel, Neta Dafni, Victor I. Kolobov, Ami Paz, and Gregory Schwartzman. Fast and simple deterministic algorithms for highly-dynamic networks. CoRR, abs/1901.04008, 2019. URL: https://doi.org/10.48550/arXiv.1901.04008.
  20. Keren Censor-Hillel, Elad Haramaty, and Zohar Karnin. Optimal dynamic distributed mis. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, pages 217-226. ACM, 2016. URL: https://doi.org/10.1145/2933057.2933083.
  21. Johanne Cohen, Jonas Lefèvre, Khaled Maâmra, Laurence Pilard, and Devan Sohier. A self-stabilizing algorithm for maximal matching in anonymous networks. Parallel Process. Lett., 26(4):1650016:1-1650016:17, 2016. URL: https://doi.org/10.1142/S012962641650016X.
  22. Johanne Cohen, George Manoussakis, Laurence Pilard, and Devan Sohier. A self-stabilizing algorithm for maximal matching in link-register model. In International Colloquium on Structural Information and Communication Complexity, pages 14-19. Springer, 2018. URL: https://doi.org/10.1007/978-3-030-01325-7_2.
  23. Richard Cole and Uzi Vishkin. Deterministic coin tossing with applications to optimal parallel list ranking. Information and Control, 70(1):32-53, 1986. URL: https://doi.org/10.1016/S0019-9958(86)80023-7.
  24. Ajoy Kumar Datta, Lawrence L. Larmore, and Toshimitsu Masuzawa. Maximum matching for anonymous trees with constant space per process. In 19th International Conference on Principles of Distributed Systems, OPODIS 2015, December 14-17, 2015, Rennes, France, volume 46 of LIPIcs, pages 16:1-16:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2015.16.
  25. Murat Demirbas, Anish Arora, Tina Nolte, and Nancy Lynch. A hierarchy-based fault-local stabilizing algorithm for tracking in sensor networks. In International Conference on Principles of Distributed Systems, pages 299-315. Springer, 2004. URL: https://doi.org/10.1007/11516798_22.
  26. Edsger W Dijkstra. Self-stabilization in spite of distributed control. In Selected writings on computing: a personal perspective, pages 41-46. Springer, 1982. Google Scholar
  27. Shlomi Dolev. Self-stabilization. MIT press, 2000. URL: http://www.cs.bgu.ac.il/%7Edolev/book/book.html.
  28. Shlomi Dolev and Ted Herman. Superstabilizing protocols for dynamic distributed systems (abstract). In Proceedings of the Fourteenth Annual ACM Symposium on Principles of Distributed Computing, Ottawa, Ontario, Canada, August 20-23, 1995, page 255. ACM, ACM, 1995. URL: https://doi.org/10.1145/224964.224993.
  29. Michael Elkin and Jian Zhang. Efficient algorithms for constructing (1+epsilon, beta)-spanners in the distributed and streaming models. Distributed Comput., 18(5):375-385, 2006. URL: https://doi.org/10.1007/s00446-005-0147-2.
  30. Manuela Fischer. Improved deterministic distributed matching via rounding. In 31st International Symposium on Distributed Computing, DISC, pages 17:1-17:15, 2017. URL: https://doi.org/10.4230/LIPIcs.DISC.2017.17.
  31. G.N. Frederickson. Data structures for on-line updating of minimum spanning trees, with applications. SIAM J. on Computing (SICOMP), 14(4):781-798, 1985. URL: https://doi.org/10.1137/0214055.
  32. Mohsen Ghaffari. An improved distributed algorithm for maximal independent set. In Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, pages 270-277. SIAM, 2016. URL: https://doi.org/10.1137/1.9781611974331.ch20.
  33. Mohsen Ghaffari. Distributed maximal independent set using small messages. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 805-820. SIAM, 2019. URL: https://doi.org/10.1137/1.9781611975482.50.
  34. Sukumar Ghosh, Arobinda Gupta, Ted Herman, and Sriram V Pemmaraju. Fault-containing self-stabilizing algorithms. In Proceedings of the fifteenth annual ACM symposium on Principles of distributed computing, pages 45-54. ACM, 1996. URL: https://doi.org/10.1145/248052.248057.
  35. Wayne Goddard, Stephen T. Hedetniemi, David Pokrass Jacobs, and Pradip K. Srimani. A robust distributed generalized matching protocol that stabilizes in linear time. In 23rd International Conference on Distributed Computing Systems Workshops (ICDCS 2003 Workshops), 19-22 May 2003, Providence, RI, USA, pages 461-465. IEEE, IEEE Computer Society, 2003. URL: https://doi.org/10.1109/ICDCSW.2003.1203595.
  36. Wayne Goddard, Stephen T. Hedetniemi, David Pokrass Jacobs, and Pradip K. Srimani. Self-stabilizing protocols for maximal matching and maximal independent sets for ad hoc networks. In 17th International Parallel and Distributed Processing Symposium (IPDPS 2003), 22-26 April 2003, Nice, France, CD-ROM/Abstracts Proceedings, page 162. IEEE, IEEE Computer Society, 2003. URL: https://doi.org/10.1109/IPDPS.2003.1213302.
  37. Maria Gradinariu and Colette Johnen. Self-stabilizing neighborhood unique naming under unfair scheduler. In European Conference on Parallel Processing, pages 458-465. Springer, 2001. URL: https://doi.org/10.1007/3-540-44681-8_67.
  38. Nabil Guellati and Hamamache Kheddouci. A survey on self-stabilizing algorithms for independence, domination, coloring, and matching in graphs. Journal of Parallel and Distributed Computing, 70(4):406-415, 2010. URL: https://doi.org/10.1016/j.jpdc.2009.11.006.
  39. Michal Hanckowiak, Michal Karonski, and Alessandro Panconesi. On the distributed complexity of computing maximal matchings. SIAM Journal on Discrete Mathematics, 15(1):41-57, 2001. URL: https://doi.org/10.1137/S0895480100373121.
  40. Stephen T Hedetniemi, David P Jacobs, and Pradip K Srimani. Maximal matching stabilizes in time o (m). Information Processing Letters, 80(5):221-223, 2001. URL: https://doi.org/10.1016/S0020-0190(01)00171-5.
  41. Maurice Herlihy, Victor Luchangco, and Mark Moir. Obstruction-free synchronization: Double-ended queues as an example. In 23rd International Conference on Distributed Computing Systems (ICDCS 2003), 19-22 May 2003, Providence, RI, USA, pages 522-529. IEEE, IEEE Computer Society, 2003. URL: https://doi.org/10.1109/ICDCS.2003.1203503.
  42. Su-Chu Hsu and Shing-Tsaan Huang. A self-stabilizing algorithm for maximal matching. Information processing letters, 43(2):77-81, 1992. URL: https://doi.org/10.1016/0020-0190(92)90015-N.
  43. Can Umut Ileri and Orhan Dagdeviren. A self-stabilizing algorithm for b-matching. Theoretical Computer Science, 753:64-75, 2019. URL: https://doi.org/10.1016/j.tcs.2018.06.042.
  44. Amos Israeli and Alon Itai. A fast and simple randomized parallel algorithm for maximal matching. Information Processing Letters, 22(2):77-80, 1986. URL: https://doi.org/10.1016/0020-0190(86)90144-4.
  45. Richard M Karp and Avi Wigderson. A fast parallel algorithm for the maximal independent set problem. Journal of the ACM (JACM), 32(4):762-773, 1985. URL: https://doi.org/10.1145/4221.4226.
  46. Masahiro Kimoto, Tatsuhiro Tsuchiya, and Tohru Kikuno. The time complexity of Hsu and Huang’s self-stabilizing maximal matching algorithm. IEICE transactions on information and systems, 93(10):2850-2853, 2010. URL: https://doi.org/10.1587/transinf.E93.D.2850.
  47. Michael König and Roger Wattenhofer. On local fixing. In International Conference On Principles Of Distributed Systems, pages 191-205. Springer, 2013. URL: https://doi.org/10.1007/978-3-319-03850-6_14.
  48. Kishore Kothapalli, Christian Scheideler, Melih Onus, and Christian Schindelhauer. Distributed coloring in O (log n) bit rounds. In 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), Proceedings, 25-29 April 2006, Rhodes Island, Greece. IEEE, 2006. URL: https://doi.org/10.1109/IPDPS.2006.1639281.
  49. Shay Kutten and Boaz Patt-Shamir. Time-adaptive self stabilization. In Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing, pages 149-158. ACM, 1997. URL: https://doi.org/10.1145/259380.259435.
  50. Shay Kutten and David Peleg. Fault-local distributed mending (extended abstract). In Proceedings of the Fourteenth Annual ACM Symposium on Principles of Distributed Computing, Ottawa, Ontario, Canada, August 20-23, 1995, pages 20-27. ACM, ACM, 1995. URL: https://doi.org/10.1145/224964.224967.
  51. Leslie Lamport. Distribution, May 1987. Email message sent to a DEC SRC bulletin board at 12:23:29 PDT on 28 May 87. URL: https://www.microsoft.com/en-us/research/publication/distribution/.
  52. Leslie Lamport. A fast mutual exclusion algorithm. ACM Transactions on Computer Systems (TOCS), 5(1):1-11, 1987. URL: https://doi.org/10.1145/7351.7352.
  53. Christoph Lenzen, Jukka Suomela, and Roger Wattenhofer. Local algorithms: Self-stabilization on speed. In Symposium on Self-Stabilizing Systems, pages 17-34. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-05118-0_2.
  54. Nathan Linial. Locality in distributed graph algorithms. SIAM J. Comput., 21(1):193-201, 1992. URL: https://doi.org/10.1137/0221015.
  55. Zvi Lotker, Boaz Patt-Shamir, and Adi Rosén. Distributed approximate matching. SIAM Journal on Computing, 39(2):445-460, 2009. URL: https://doi.org/10.1137/080714403.
  56. Michael Luby. A simple parallel algorithm for the maximal independent set problem. SIAM journal on computing, 15(4):1036-1053, 1986. URL: https://doi.org/10.1137/0215074.
  57. Fredrik Manne, Morten Mjelde, Laurence Pilard, and Sébastien Tixeuil. A new self-stabilizing maximal matching algorithm. Theoretical Computer Science, 410(14):1336-1345, 2009. URL: https://doi.org/10.1016/j.tcs.2008.12.022.
  58. Fredrik Manne, Morten Mjelde, Laurence Pilard, and Sébastien Tixeuil. A self-stabilizing 23-approximation algorithm for the maximum matching problem. Theoretical Computer Science, 412(40):5515-5526, 2011. URL: https://doi.org/10.1016/j.tcs.2011.05.019.
  59. Darya Melnyk, Jukka Suomela, and Neven Villani. Mending partial solutions with few changes. CoRR, abs/2209.05363, 2022. URL: https://doi.org/10.48550/arXiv.2209.05363.
  60. Ofer Neiman and Shay Solomon. Simple deterministic algorithms for fully dynamic maximal matching. ACM Trans. Algorithms, 12(1):7:1-7:15, 2016. URL: https://doi.org/10.1145/2700206.
  61. Alessandro Panconesi and Romeo Rizzi. Some simple distributed algorithms for sparse networks. Distributed Comput., 14(2):97-100, 2001. URL: https://doi.org/10.1007/PL00008932.
  62. Alex Scott, Peter Jeavons, and Lei Xu. Feedback from nature: an optimal distributed algorithm for maximal independent set selection. In Proceedings of the 2013 ACM symposium on Principles of distributed computing, pages 147-156, 2013. URL: https://doi.org/10.1145/2484239.2484247.
  63. Zhengnan Shi, Wayne Goddard, and Stephen T Hedetniemi. An anonymous self-stabilizing algorithm for 1-maximal independent set in trees. Information Processing Letters, 91(2):77-83, 2004. URL: https://doi.org/10.1016/j.ipl.2004.03.010.
  64. Gerard Tel. Maximal matching stabilizes in quadratic time. Information Processing Letters, 49(6):271-272, 1994. URL: https://doi.org/10.1016/0020-0190(94)90098-1.
  65. Volker Turau. Making randomized algorithms self-stabilizing. In Structural Information and Communication Complexity - 26th International Colloquium, SIROCCO 2019, L'Aquila, Italy, July 1-4, 2019, Proceedings, pages 309-324, 2019. URL: https://doi.org/10.1007/978-3-030-24922-9_21.
  66. Mirjam Wattenhofer and Roger Wattenhofer. Distributed weighted matching. In International Symposium on Distributed Computing, pages 335-348. Springer, 2004. URL: https://doi.org/10.1007/978-3-540-30186-8_24.
  67. Elizabeth Lee Wilmer. Exact rates of convergence for some simple non-reversible Markov chains. PhD thesis, Department of Mathematics, Harvard University, 1999. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact