We present the first polynomial self-stabilizing algorithm for finding a (2/3)-approximation of a maximum matching in a general graph. The previous best known algorithm has been presented by Manne et al. and has a sub-exponential time complexity under the distributed adversarial daemon. Our new algorithm is an adaptation of the Manne et al. algorithm and works under the same daemon, but with a time complexity in O(n^3) moves. Moreover, our algorithm only needs one more boolean variable than the previous one, thus as in the Manne et al. algorithm, it only requires a constant amount of memory space (three identifiers and two booleans per node).
@InProceedings{cohen_et_al:LIPIcs.OPODIS.2016.11, author = {Cohen, Johanne and Ma\^{a}mra, Khaled and Manoussakis, George and Pilard, Laurence}, title = {{Polynomial Self-Stabilizing Maximum Matching Algorithm with Approximation Ratio 2/3}}, booktitle = {20th International Conference on Principles of Distributed Systems (OPODIS 2016)}, pages = {11:1--11:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-031-6}, ISSN = {1868-8969}, year = {2017}, volume = {70}, editor = {Fatourou, Panagiota and Jim\'{e}nez, Ernesto and Pedone, Fernando}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2016.11}, URN = {urn:nbn:de:0030-drops-70808}, doi = {10.4230/LIPIcs.OPODIS.2016.11}, annote = {Keywords: Self-Stabilization, Distributed Algorithm, Fault Tolerance, Matching} }
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