Optimal maintenance of a spanning tree
Journal of the ACM (JACM)
The generalized deadlock resolution problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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The deadlock resolution problem can be informally stated as follows. There exists a set of actions, generated at different times, with some complex and contradictory precedence constraints between their executions. To resolve a deadlock, some of the actions need to be aborted; this enables to execute the remaining ones. This problem naturally arises in the context of distributed systems, e.g. communication networks, distributed operating systems and distributed databases, where actions are generated by many processors, and are not coordinated by a central controller. In this paper, we are concerned with efficient distributed algorithms (protocols) for resolution of dynamic deadlocks. Such resolution protocols must operate on-line without any knowledge of the future and using only local information. The main contribution of the paper is a reduction of the most general dynamic deadlock resolution problem to a conceptually simpler static problem, in which all actions are known a priori. The complexity of our reduction is O (m + n logn) in communication and O (n) in time, where n is the number of actions and m is total number of constraints. Since the static deadlock resolution requires at least Ω(m + n logn) in communication and Ω(n) in time, our reduction essentially shows that the resolution of dynamic deadlocks is not any harder than resolution of the static ones. We also show here a simple and optimal algorithm for the static problem, which, together with the above reduction, yields an optimal dynamic deadlock resolution protocol.