Electing a leader in a synchronous ring
Journal of the ACM (JACM)
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Optimal lower bounds for some distributed algorithms for a complete network of processors
Theoretical Computer Science
A trade-off between information and communication in broadcast protocols
Journal of the ACM (JACM)
Time-optimal leader election in general networks
Journal of Parallel and Distributed Computing
Time and message bounds for election in synchronous and asynchronous complete networks
SIAM Journal on Computing
Introduction to distributed algorithms
Introduction to distributed algorithms
Randomized algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Distributed Algorithms
The cougar approach to in-network query processing in sensor networks
ACM SIGMOD Record
On the Complexities of the Leader Election Algorithms
ICCI '93 Proceedings of the Fifth International Conference on Computing and Information
Timing-sync protocol for sensor networks
Proceedings of the 1st international conference on Embedded networked sensor systems
Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing)
Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing)
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
The Akamai network: a platform for high-performance internet applications
ACM SIGOPS Operating Systems Review
Knowledge, level of symmetry, and time of leader election
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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Electing a leader is a fundamental task in distributed computing. In its implicit version, only the leader must know who is the elected leader. This paper focuses on studying the message and time complexity of randomized implicit leader election in synchronous distributed networks. Surprisingly, the most "obvious" complexity bounds have not been proven for randomized algorithms. The "obvious" lower bounds of Ω(m) messages (m is the number of edges in the network) and Ω(D) time (D is the network diameter) are non-trivial to show for randomized (Monte Carlo) algorithms. (Recent results that show that even Ω(n) (n is the number of nodes in the network) is not a lower bound on the messages in complete networks, make the above bounds somewhat less obvious). To the best of our knowledge, these basic lower bounds have not been established even for deterministic algorithms (except for the limited case of comparison algorithms, where it was also required that some nodes may not wake up spontaneously, and that D and n were not known). We establish these fundamental lower bounds in this paper for the general case, even for randomized Monte Carlo algorithms. Our lower bounds are universal in the sense that they hold for all universal algorithms (such algorithms should work for all graphs), apply to every D, m, and n, and hold even if D, m, and n are known, all the nodes wake up simultaneously, and the algorithms can make anyuse of node's identities. To show that these bounds are tight, we present an O(m) messages algorithm. An O(D) time algorithm is known. A slight adaptation of our lower bound technique gives rise to an Ω(m) message lower bound for randomized broadcast algorithms. An interesting fundamental problem is whether both upper bounds (messages and time) can be reached simultaneously in the randomized setting for all graphs. (The answer is known to be negative in the deterministic setting). We answer this problem partially by presenting a randomized algorithm that matches both complexities in some cases. This already separates (for some cases) randomized algorithms from deterministic ones. As first steps towards the general case, we present several universal leader election algorithms with bounds that trade-off messages versus time. We view our results as a step towards understanding the complexity of universal leader election in distributed networks.