Communication Efficiency in Self-Stabilizing Silent Protocols

Stephane Devismes, Toshimitsu Masuzawa, Sebastien Tixeuil
2009 2009 29th IEEE International Conference on Distributed Computing Systems  
Self-stabilization is a general paradigm to provide forward recovery capabilities to distributed systems and networks. Intuitively, a protocol is selfstabilizing if it is able to recover without external intervention from any catastrophic transient failure. In this paper, our focus is to lower the communication complexity of self-stabilizing protocols below the need of checking every neighbor forever. In more details, the contribution of the paper is threefold: (i) We provide new complexity
more » ... ures for communication efficiency of self-stabilizing protocols, especially in the stabilized phase or when there are no faults, (ii) On the negative side, we show that for non-trivial problems such as coloring, maximal matching, and maximal independent set, it is impossible to get (deterministic or probabilistic) self-stabilizing solutions where every participant communicates with less than every neighbor in the stabilized phase, and (iii) On the positive side, we present protocols for coloring, maximal matching, and maximal independent set such that a fraction of the participants communicates with exactly one neighbor in the stabilized phase. Résumé : L'auto-stabilisation est un paradigme général pour assurer la reprise sur erreur dans les réseaux et les systèmes distribués. Un algorithme réparti est autostabilisant si, après que des fautes et des attaques aient frappé le système et l'aient placé dans unétat quelconque, le système corrige cette situation catastrophique sans intervention extérieure en temps fini. Dans cet article, nous nous concentrons sur la complexité des communications des algorithmes auto-stabilisants au delà du besoin de vérifier infiment souvent tous les voisins de chaque processus. La contribution de l'article peutêtre résumée en trois points principaux: (i) nous proposons de nouvelles mesures de complexité pour les communications des protocoles auto-stabilisants, e particulier dans la phase stabilisée ou quand il n'y a pas de fautes ; (ii) nous montrons que pour des problèmes non-triviaux tels que le coloriage, le mariage maximal, et l'ensemble maximal indépendant, il est impossible d'obtenir des solutions (déterministes ou probabilistes) auto-stabilisantes ou chaque participant communique avec moins que tous ses voisins dans la phase stabilisée ; (iii) nous présentons des protocoles pour le coloriage, le mariage maximal, et l'ensemble maximal indépendant tels qu'une fraction des participants communique avec exactement un voisin lors de la phase stabilisée. Mots-clés : auto-stabilisation, bornes inférieures, complexité des communications, coloriage, mariage maximal, ensemble maximal indépendant Communication Efficiency in Self-stabilizing Silent Protocols 3 1 Introduction Self-stabilization [8] is a general paradigm to provide forward recovery capabilities to distributed systems and networks. Intuitively, a protocol is self-stabilizing if it is able to recover without external intervention from any catastrophic transient failure. Among the many self-stabilizing solutions available today [9], the most useful ones for real networks are those that admit efficient implementations. Most of the literature is dedicated to improving efficiency after failures occur, i.e., minimizing the stabilization time -the maximum amount of time one has to wait before failure recovery. While this metric is meaningful to evaluate the efficiency in the presence of failures, it fails at capturing the overhead of self-stabilization when there are no faults, or after stabilization. In order to take forward recovery actions in case of failures, a self-stabilizing protocol has to gather information from other nodes in order to detect inconsistencies. Of course, a global communication mechanism will lead to a large coverage of anomaly detection [15] at the expense of an extremely expensive solution when there are no faults, since information about every participant has to be repetitively sent to every other participant. As pointed out in [5] , the amount of information that has to be gatherered highly depends on the task to be solved if only the output of the protocol is to be used for such anomaly detection. The paper also points out that more efficient schemes could be available for some particular implementations. However, to the best of our knowledge, the minimal amount of communicated information in self-stabilizing systems is still fully local [3, 4, 5] : when there are no faults, every participant has to communicate with every other neighbor repetitively. In this paper, our focus is to lower the communication complexity of self-stabilizing protocols below the need of checking every neighbor. A quick observation shows that non-existent communication is impossible in the context of self-stabilization: the initial configuration of the network could be such that the specification is violated while no participant is sending nor getting neighboring information, resulting in a deadlock. On the other side, there exist problems (such as coloring, maximal matching, maximal independent set) that admit solutions where participants only have to communicate with their full set of neighbors. We investigate the possibility of intermediate solutions (i.e. where participants communicate repetitively only with a strict subset of their neighbors) that would lead to more efficient implementations in stabilized phase or when there are no faults. Good candidates for admitting such interesting complexity solutions are silent protocols [10]: a silent protocol is a selfstabilizing protocol that exhibits the additionnal property that after stabilization, communication is fixed between neighbors (that is, neighbors repetitively commu-RR n 6731
doi:10.1109/icdcs.2009.24 dblp:conf/icdcs/DevismesMT09 fatcat:lk6nd5u4vjgebiy4pia7snywje